Question

How do you multiply and simplify `\frac { 4x } { 20x + 4} \cdot \frac { 35x + 7} { 4}`?

Answer 1

See the entire solution process below:

Explanation:

First, we can rewrite this expression as:

`(4x)/(4(5x + 1)) * (7(5x + 1))/4`

Next, we can cancel common terms in the numerators and denominators of the fractions:

`(color(red)(cancel(color(black)(4)))x)/(color(red)(cancel(color(black)(4)))(color(blue)(cancel(color(black)(5x + 1))))) * (7(color(blue)(cancel(color(black)(5x + 1)))))/4 = (7x)/4`

The restriction, to ensure we do not divide by `0` is:

`x != -1/5`