Question

How do you find the quotient of `(14x^2+7x)div7x`?

Answer 1

`2x +1`

Explanation:

You can compare this to

`3x(5x+4) = 15x^2 +12x`

where the `" "3x" "` is multiplied by both terms inside the bracket using the distributive law,

`(14x^2 +7x)div 7x" "` can be written as `" "1/(7x)(14x^2 +7x)`

Or as `" "(14x^2 +7x)/(7x)`

Or as separate terms: `" "(14x^2)/(7x) +(7x)/(7x)`

Whichever you choose, each of the terms has to be divided by `7x`

`=2x +1`

Answer 2

See a solution process below:

Explanation:

First, rewrite the expression as:

`(14x^2 + 7x)/(7x) => (14x^2)/(7x) + (7x)/(7x) => (14x^2)/(7x) + 1`

Next, factor `7x` out of the numerator and denominator in the fraction on the left giving:

`(7x xx 2x)/(7x xx 1) + 1 => (color(red)(cancel(color(black)(7x))) xx 2x)/(color(red)(cancel(color(black)(7x))) xx 1) + 1 => (2x)/1 + 1 =>`

`2x + 1`

However, from the original expression we cannot divide by `0` therefore we need the exclusion:

Where: `7x != 0` or `x != 0`