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Pictures sent I solved problem and would like toKnowIf I did it correctly

Pictures sent I solved problem and would like toKnowIf I did it correctly-example-1

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Step-by-step explanation

Since we have the expression:


(7x+42)/(x^2+13x+42)

Factoring 7x + 42:


\mathrm{Rewrite\:}42\mathrm{\:as\:}7\cdot \:6
=7x+7\cdot \:6

Factor out common term 7:


=7\left(x+6\right)
=(7\left(x+6\right))/(x^2+13x+42)

Factor x^2+13x+42:

Breaking the expression into groups:


=\left(x^2+6x\right)+\left(7x+42\right)

Factor out x from x^2+6x:


=x\left(x+6\right)

Factor out 7 from 7x + 42:


=x\left(x+6\right)+7\left(x+6\right)

Factor out common term x+6:


=(7\left(x+6\right))/(\left(x+6\right)\left(x+7\right))
\mathrm{Cancel\:the\:common\:factor:}\:x+6

The final expression is as follows:


=(7)/(x+7)

User Nataliastanko
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