Pre-Algebra Examples

Solve Using the Square Root Property (x-4)/x=3/(x^2)+(3x^2+27x+60)/(2x^2)
Step 1
Factor each term.
Tap for more steps...
Step 1.1
Factor out of .
Tap for more steps...
Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.1.4
Factor out of .
Step 1.1.5
Factor out of .
Step 1.2
Factor.
Tap for more steps...
Step 1.2.1
Factor using the AC method.
Tap for more steps...
Step 1.2.1.1
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 1.2.1.2
Write the factored form using these integers.
Step 1.2.2
Remove unnecessary parentheses.
Step 2
Find the LCD of the terms in the equation.
Tap for more steps...
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 two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
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
Since has no factors besides and .
is a prime number
Step 2.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.7
The factor for is itself.
occurs time.
Step 2.8
The factors for are , which is multiplied by each other times.
occurs times.
Step 2.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.10
Multiply by .
Step 2.11
The LCM for is the numeric part multiplied by the variable part.
Step 3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Rewrite using the commutative property of multiplication.
Step 3.2.2
Combine and .
Step 3.2.3
Cancel the common factor of .
Tap for more steps...
Step 3.2.3.1
Factor out of .
Step 3.2.3.2
Cancel the common factor.
Step 3.2.3.3
Rewrite the expression.
Step 3.2.4
Apply the distributive property.
Step 3.2.5
Multiply by .
Step 3.2.6
Apply the distributive property.
Step 3.2.7
Multiply by by adding the exponents.
Tap for more steps...
Step 3.2.7.1
Move .
Step 3.2.7.2
Multiply by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Simplify each term.
Tap for more steps...
Step 3.3.1.1
Rewrite using the commutative property of multiplication.
Step 3.3.1.2
Multiply .
Tap for more steps...
Step 3.3.1.2.1
Combine and .
Step 3.3.1.2.2
Multiply by .
Step 3.3.1.3
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.3.1
Cancel the common factor.
Step 3.3.1.3.2
Rewrite the expression.
Step 3.3.1.4
Rewrite using the commutative property of multiplication.
Step 3.3.1.5
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.5.1
Factor out of .
Step 3.3.1.5.2
Cancel the common factor.
Step 3.3.1.5.3
Rewrite the expression.
Step 3.3.1.6
Cancel the common factor of .
Tap for more steps...
Step 3.3.1.6.1
Cancel the common factor.
Step 3.3.1.6.2
Rewrite the expression.
Step 3.3.1.7
Apply the distributive property.
Step 3.3.1.8
Multiply by .
Step 3.3.1.9
Expand using the FOIL Method.
Tap for more steps...
Step 3.3.1.9.1
Apply the distributive property.
Step 3.3.1.9.2
Apply the distributive property.
Step 3.3.1.9.3
Apply the distributive property.
Step 3.3.1.10
Simplify and combine like terms.
Tap for more steps...
Step 3.3.1.10.1
Simplify each term.
Tap for more steps...
Step 3.3.1.10.1.1
Multiply by by adding the exponents.
Tap for more steps...
Step 3.3.1.10.1.1.1
Move .
Step 3.3.1.10.1.1.2
Multiply by .
Step 3.3.1.10.1.2
Multiply by .
Step 3.3.1.10.1.3
Multiply by .
Step 3.3.1.10.2
Add and .
Step 3.3.2
Add and .
Step 4
Solve the equation.
Tap for more steps...
Step 4.1
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from both sides of the equation.
Step 4.1.3
Subtract from .
Step 4.1.4
Subtract from .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Factor the left side of the equation.
Tap for more steps...
Step 4.3.1
Factor out of .
Tap for more steps...
Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Factor out of .
Step 4.3.1.3
Rewrite as .
Step 4.3.1.4
Factor out of .
Step 4.3.1.5
Factor out of .
Step 4.3.2
Factor.
Tap for more steps...
Step 4.3.2.1
Factor using the AC method.
Tap for more steps...
Step 4.3.2.1.1
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 4.3.2.1.2
Write the factored form using these integers.
Step 4.3.2.2
Remove unnecessary parentheses.
Step 4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.5
Set equal to and solve for .
Tap for more steps...
Step 4.5.1
Set equal to .
Step 4.5.2
Subtract from both sides of the equation.
Step 4.6
Set equal to and solve for .
Tap for more steps...
Step 4.6.1
Set equal to .
Step 4.6.2
Subtract from both sides of the equation.
Step 4.7
The final solution is all the values that make true.