Basic Math Examples

Simplify ((y^2-9)/(4y+12))÷((2y^2-12y+18)/(8y+24))
Step 1
To divide by a fraction, multiply by its reciprocal.
Step 2
Simplify the numerator.
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Step 2.1
Rewrite as .
Step 2.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3
Simplify terms.
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Step 3.1
Factor out of .
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Step 3.1.1
Factor out of .
Step 3.1.2
Factor out of .
Step 3.1.3
Factor out of .
Step 3.2
Cancel the common factor of .
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Step 3.2.1
Cancel the common factor.
Step 3.2.2
Rewrite the expression.
Step 3.3
Cancel the common factor of and .
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Step 3.3.1
Factor out of .
Step 3.3.2
Factor out of .
Step 3.3.3
Factor out of .
Step 3.3.4
Cancel the common factors.
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Step 3.3.4.1
Factor out of .
Step 3.3.4.2
Factor out of .
Step 3.3.4.3
Factor out of .
Step 3.3.4.4
Factor out of .
Step 3.3.4.5
Factor out of .
Step 3.3.4.6
Cancel the common factor.
Step 3.3.4.7
Rewrite the expression.
Step 3.4
Factor out of .
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Step 3.4.1
Factor out of .
Step 3.4.2
Factor out of .
Step 3.4.3
Factor out of .
Step 4
Factor using the perfect square rule.
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Step 4.1
Rewrite as .
Step 4.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 4.3
Rewrite the polynomial.
Step 4.4
Factor using the perfect square trinomial rule , where and .
Step 5
Reduce the expression by cancelling the common factors.
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Step 5.1
Cancel the common factor of .
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Step 5.1.1
Factor out of .
Step 5.1.2
Cancel the common factor.
Step 5.1.3
Rewrite the expression.
Step 5.2
Cancel the common factor of .
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Step 5.2.1
Cancel the common factor.
Step 5.2.2
Rewrite the expression.