Question

How do you multiply `\frac { 7b + 35} { 7} \cdot \frac { b + 8} { b + 5}`?

Answer 1

See a solution process below:

Explanation:

First, factor the numerator of the fraction on the left as:

`((7 * b) + (7 * 5))/7 * (b + 8)/(b + 5) =>`

`(7(b + 5))/7 * (b + 8)/(b + 5)`

Next, cancel common terms in the numerators and denominators:

`(color(red)(cancel(color(black)(7)))color(blue)(cancel(color(black)((b + 5)))))/color(red)(cancel(color(black)(7))) * (b + 8)/color(blue)(cancel(color(black)(b + 5))) =>`

`1/1 * (b + 8)/1 =>`

`b + 8`

However, because we cannot divide by `0` we need to exclude where:

`b + 5 != 0`

Or

`b != -5`

So the solution is: `b + 8` where `b != -5`