Question

How do you multiply and simplify `\frac { x ^ { 2} + 12x + 35} { x + 5} \cdot \frac { 6} { 6x + 42}`?

Answer 1

See a solution process below:

Explanation:

First, factor the numerator of the fraction on the left and the denominator of the fraction on the right:

`((x + 5)(x + 7))/(x + 5) * 6/(6(x + 7)`

Now, cancel common terms in the numerator and denominators:

`((color(red)(cancel(color(black)(x + 5))))(color(blue)(cancel(color(black)(x + 7)))))/color(red)(cancel(color(black)(x + 5))) * color(purple)(cancel(color(black)(6)))/(color(purple)(cancel(color(black)(6))color(blue)(cancel(color(black)((x + 7))) =>`

`1`

Where `x != -5` and `x != -7`