Basic Math Examples

Solve for a 2/(5-a)=(a+4)/(a-5)
Step 1
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Step 2
Solve the equation for .
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Step 2.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2.2
Simplify .
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Step 2.2.1
Rewrite.
Step 2.2.2
Simplify by adding zeros.
Step 2.2.3
Expand using the FOIL Method.
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Step 2.2.3.1
Apply the distributive property.
Step 2.2.3.2
Apply the distributive property.
Step 2.2.3.3
Apply the distributive property.
Step 2.2.4
Simplify and combine like terms.
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Step 2.2.4.1
Simplify each term.
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Step 2.2.4.1.1
Multiply by .
Step 2.2.4.1.2
Multiply by by adding the exponents.
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Step 2.2.4.1.2.1
Move .
Step 2.2.4.1.2.2
Multiply by .
Step 2.2.4.1.3
Multiply by .
Step 2.2.4.2
Subtract from .
Step 2.3
Simplify .
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Step 2.3.1
Apply the distributive property.
Step 2.3.2
Multiply by .
Step 2.4
Move all terms containing to the left side of the equation.
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Step 2.4.1
Subtract from both sides of the equation.
Step 2.4.2
Subtract from .
Step 2.5
Add to both sides of the equation.
Step 2.6
Add and .
Step 2.7
Factor the left side of the equation.
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Step 2.7.1
Factor out of .
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Step 2.7.1.1
Reorder and .
Step 2.7.1.2
Factor out of .
Step 2.7.1.3
Factor out of .
Step 2.7.1.4
Rewrite as .
Step 2.7.1.5
Factor out of .
Step 2.7.1.6
Factor out of .
Step 2.7.2
Factor.
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Step 2.7.2.1
Factor using the AC method.
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Step 2.7.2.1.1
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 2.7.2.1.2
Write the factored form using these integers.
Step 2.7.2.2
Remove unnecessary parentheses.
Step 2.8
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.9
Set equal to and solve for .
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Step 2.9.1
Set equal to .
Step 2.9.2
Add to both sides of the equation.
Step 2.10
Set equal to and solve for .
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Step 2.10.1
Set equal to .
Step 2.10.2
Subtract from both sides of the equation.
Step 2.11
The final solution is all the values that make true.
Step 3
Exclude the solutions that do not make true.