Simplify ((75n^2-147)/(5n^2-12n+7))÷((35n^2+34n-21)/(n^2-8n+7))

Math
To divide by a fraction, multiply by its reciprocal.
Simplify the numerator.
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Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Factor using the AC method.
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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 .
Write the factored form using these integers.
Factor by grouping.
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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Tap for more steps…
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Simplify ((75n^2-147)/(5n^2-12n+7))÷((35n^2+34n-21)/(n^2-8n+7))

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