Basic Math Examples

Solve for a 9/(a^2)+16/(a^2-25)=1
Step 1
Factor each term.
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Step 1.1
Rewrite as .
Step 1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Since contains both numbers and variables, there are four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.
Steps to find the LCM for are:
1. Find the LCM for the numeric part .
2. Find the LCM for the variable part .
3. Find the LCM for the compound variable part .
4. Multiply each LCM together.
Step 2.3
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2.4
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.6
The factors for are , which is multiplied by each other times.
occurs times.
Step 2.7
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.8
Multiply by .
Step 2.9
The factor for is itself.
occurs time.
Step 2.10
The factor for is itself.
occurs time.
Step 2.11
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.12
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify each term.
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Step 3.2.1.1
Cancel the common factor of .
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Step 3.2.1.1.1
Factor out of .
Step 3.2.1.1.2
Cancel the common factor.
Step 3.2.1.1.3
Rewrite the expression.
Step 3.2.1.2
Expand using the FOIL Method.
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Step 3.2.1.2.1
Apply the distributive property.
Step 3.2.1.2.2
Apply the distributive property.
Step 3.2.1.2.3
Apply the distributive property.
Step 3.2.1.3
Combine the opposite terms in .
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Step 3.2.1.3.1
Reorder the factors in the terms and .
Step 3.2.1.3.2
Add and .
Step 3.2.1.3.3
Add and .
Step 3.2.1.4
Simplify each term.
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Step 3.2.1.4.1
Multiply by .
Step 3.2.1.4.2
Multiply by .
Step 3.2.1.5
Apply the distributive property.
Step 3.2.1.6
Multiply by .
Step 3.2.1.7
Cancel the common factor of .
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Step 3.2.1.7.1
Factor out of .
Step 3.2.1.7.2
Cancel the common factor.
Step 3.2.1.7.3
Rewrite the expression.
Step 3.2.2
Add and .
Step 3.3
Simplify the right side.
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Step 3.3.1
Multiply by .
Step 3.3.2
Apply the distributive property.
Step 3.3.3
Multiply by by adding the exponents.
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Step 3.3.3.1
Multiply by .
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Step 3.3.3.1.1
Raise to the power of .
Step 3.3.3.1.2
Use the power rule to combine exponents.
Step 3.3.3.2
Add and .
Step 3.3.4
Move to the left of .
Step 3.3.5
Expand using the FOIL Method.
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Step 3.3.5.1
Apply the distributive property.
Step 3.3.5.2
Apply the distributive property.
Step 3.3.5.3
Apply the distributive property.
Step 3.3.6
Simplify and combine like terms.
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Step 3.3.6.1
Simplify each term.
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Step 3.3.6.1.1
Multiply by by adding the exponents.
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Step 3.3.6.1.1.1
Multiply by .
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Step 3.3.6.1.1.1.1
Raise to the power of .
Step 3.3.6.1.1.1.2
Use the power rule to combine exponents.
Step 3.3.6.1.1.2
Add and .
Step 3.3.6.1.2
Move to the left of .
Step 3.3.6.1.3
Multiply by by adding the exponents.
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Step 3.3.6.1.3.1
Move .
Step 3.3.6.1.3.2
Multiply by .
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Step 3.3.6.1.3.2.1
Raise to the power of .
Step 3.3.6.1.3.2.2
Use the power rule to combine exponents.
Step 3.3.6.1.3.3
Add and .
Step 3.3.6.1.4
Multiply by .
Step 3.3.6.2
Add and .
Step 3.3.6.3
Add and .
Step 4
Solve the equation.
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Step 4.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.2
Move all the expressions to the left side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Add to both sides of the equation.
Step 4.3
Subtract from .
Step 4.4
Substitute into the equation. This will make the quadratic formula easy to use.
Step 4.5
Factor using the AC method.
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Step 4.5.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.5.2
Write the factored form using these integers.
Step 4.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.7
Set equal to and solve for .
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Step 4.7.1
Set equal to .
Step 4.7.2
Add to both sides of the equation.
Step 4.8
Set equal to and solve for .
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Step 4.8.1
Set equal to .
Step 4.8.2
Add to both sides of the equation.
Step 4.9
The final solution is all the values that make true.
Step 4.10
Substitute the real value of back into the solved equation.
Step 4.11
Solve the first equation for .
Step 4.12
Solve the equation for .
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Step 4.12.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.12.2
Simplify .
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Step 4.12.2.1
Rewrite as .
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Step 4.12.2.1.1
Factor out of .
Step 4.12.2.1.2
Rewrite as .
Step 4.12.2.2
Pull terms out from under the radical.
Step 4.12.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.12.3.1
First, use the positive value of the to find the first solution.
Step 4.12.3.2
Next, use the negative value of the to find the second solution.
Step 4.12.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 4.13
Solve the second equation for .
Step 4.14
Solve the equation for .
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Step 4.14.1
Remove parentheses.
Step 4.14.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.14.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.14.3.1
First, use the positive value of the to find the first solution.
Step 4.14.3.2
Next, use the negative value of the to find the second solution.
Step 4.14.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 4.15
The solution to is .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: