Question

Are these correct?
simplifying rational expressions.

Answer 1

1.)

100/x + 100/(x + 1)

100/x * (x + 1)/(x + 1) = (100x + 100)/(x^2 + x)
100/(x + 1) * x/x = 100x/(x^2 + x)

(100x + 100)/(x^2 + x) + 100x/(x^2 + x) =
(200x^2 + 100)/(x^2 + x)

Answer 2

2.)

15/(x + 8) + 10/x

15/(x + 8) * x/x = (15x + 120)/(x^2 + 8x)
10/x * (x + 8)/(x + 8) = (10x + 80)/(x^2 + 8x)

(15x + 120)/(x^2 + 8x) + (10x + 80)/(x^2 + 8x) = (25x + 200)/(x^2 + 8x)

Answer 3

The first one is wrong. Let me show you my work.

Answer 4

\[\frac{ 100 }{ x }+\frac{ 100 }{ x+1 }=\frac{ 100x+100+100x }{ x(x+1) }=\frac{ 200x+100 }{ x^2+x }\]

Answer 5

The second one is also wrong. Let me show you my work.

Answer 6

\[\frac{ 15 }{ x+8 }+\frac{ 10 }{ x }=\frac{ 15x+10x+80 }{ x^2+8x }=\frac{ 25x+80 }{ x^2+8x }\]

Answer 7

Wait, how did you get x^2 + x out of that? I thought when adding fractions the denominator is supposed to stay the same?

Answer 8

@Idealist10

Answer 9

Yes, it stays the same. But it looks nicer because x(x+1)=x^2+x, you get it?

Answer 10

You just distribute x(x+1) to get x^2+x.

Answer 11

Oh, I see now. So my answer was correct, it just wasn't completely simplified.