Question

To divide 7/x+2 by x-2/14 you can multiply 7/x+2 by which of the following

Answer 1

`\huge\boxed{(14)/(x-2)}`

To divide fractions, you multiply the dividend by the reciprocal of the divisor. In other words, you flip the numerator and denominator of the second fraction, then multiply across.

In this case, the dividend is
`\displaystyle(7)/(x+2)` and the divisor is
`\displaystyle(x-2)/(14)`.

Start by getting the reciprocal of the divisor:

`\displaystyle{(7)/(x+2)/(x-2)/(14)=(7)/(x+2)*\boxed{(14)/(x-2)}}`

This fraction is the answer to the question itself, but we're going to solve all the way just for fun.

Multiply across:

`\displaystyle{(7*14)/((x+2)(x-2))=(98)/((x+2)(x-2))}`

We'll use the FOIL method to multiply the two binomials in the denominator:

First:
`x*x=\bf{x^2}`

Outside:
`x*-2=\bf{-2x}`

Inside:
`2*x=\bf{2x}`

Last:
`2*-2=\bf{-4}`

`\displaystyle{(98)/(x^2-2x+2x-4)=\boxed{(98)/(x^2-4)}}`