Question

Simplify.

Answer 1

x / 7x + x^2

Answer 2

I know its either A or C, I just need help finding the other part.

Answer 3

What do you get when you factor 7x + x^2

Answer 4

x(7 + x) ?

Answer 5

good, then the x terms cancel

Answer 6

\[\Large \frac{x}{7x+x^2}\]
\[\Large \frac{x}{x(7+x)}\]
\[\Large \frac{\cancel{x}}{\cancel{x}(7+x)}\]
\[\Large \frac{1}{7+x}\]

Answer 7

To make sure the first and last expressions are 100% equivalent, we need to make sure that x is not 0 and x is not -7

we do this to avoid division by zero errors in the first expression

Answer 8

you find x = 0 and x = 7 by setting the denominator equal to zero and solving

x(7+x) = 0

x = 0 or 7+x = 0

and I'm sure you see how to finish up

Answer 9

So it would be C?

Answer 10

correct

Answer 11

Thank you very much!

Answer 12

if we left out x =/= 0, then x = 0 would work in the last expression

BUT it wouldn't work in the first one

so this would throw off the fact the first and last expressions were 100% equal

Answer 13

but excluding 0 fixes that

Answer 14

you're welcome