EXPLANATION
Since we have the expression:
[tex]\frac{7x+42}{x^2+13x+42}[/tex]
Factoring 7x + 42:
[tex]\mathrm{Rewrite\:}42\mathrm{\:as\:}7\cdot \:6[/tex][tex]=7x+7\cdot \:6[/tex]
Factor out common term 7:
[tex]=7\left(x+6\right)[/tex][tex]=\frac{7\left(x+6\right)}{x^2+13x+42}[/tex]
Factor x^2+13x+42:
Breaking the expression into groups:
[tex]=\left(x^2+6x\right)+\left(7x+42\right)[/tex]
Factor out x from x^2+6x:
[tex]=x\left(x+6\right)[/tex]
Factor out 7 from 7x + 42:
[tex]=x\left(x+6\right)+7\left(x+6\right)[/tex]
Factor out common term x+6:
[tex]=\frac{7\left(x+6\right)}{\left(x+6\right)\left(x+7\right)}[/tex][tex]\mathrm{Cancel\:the\:common\:factor:}\:x+6[/tex]
The final expression is as follows:
[tex]=\frac{7}{x+7}[/tex]
