Simplify (5x+6)÷((25x^2-36)/(5x^2+29x-42))

Math
(5x+6)÷25×2-365×2+29x-42
To divide by a fraction, multiply by its reciprocal.
(5x+6)5×2+29x-4225×2-36
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅-42=-210 and whose sum is b=29.
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Factor 29 out of 29x.
(5x+6)5×2+29(x)-4225×2-36
Rewrite 29 as -6 plus 35
(5x+6)5×2+(-6+35)x-4225×2-36
Apply the distributive property.
(5x+6)5×2-6x+35x-4225×2-36
(5x+6)5×2-6x+35x-4225×2-36
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(5x+6)(5×2-6x)+35x-4225×2-36
Factor out the greatest common factor (GCF) from each group.
(5x+6)x(5x-6)+7(5x-6)25×2-36
(5x+6)x(5x-6)+7(5x-6)25×2-36
Factor the polynomial by factoring out the greatest common factor, 5x-6.
(5x+6)(5x-6)(x+7)25×2-36
(5x+6)(5x-6)(x+7)25×2-36
Simplify the denominator.
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Rewrite 25×2 as (5x)2.
(5x+6)(5x-6)(x+7)(5x)2-36
Rewrite 36 as 62.
(5x+6)(5x-6)(x+7)(5x)2-62
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=5x and b=6.
(5x+6)(5x-6)(x+7)(5x+6)(5x-6)
(5x+6)(5x-6)(x+7)(5x+6)(5x-6)
Reduce the expression by cancelling the common factors.
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Cancel the common factor of 5x+6.
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Cancel the common factor.
(5x+6)(5x-6)(x+7)(5x+6)(5x-6)
Rewrite the expression.
(5x-6)(x+7)5x-6
(5x-6)(x+7)5x-6
Cancel the common factor of 5x-6.
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Cancel the common factor.
(5x-6)(x+7)5x-6
Divide x+7 by 1.
x+7
x+7
x+7
Simplify (5x+6)÷((25x^2-36)/(5x^2+29x-42))

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