Question

Anyone wanna check my work for my rational question?

Answer 1

\[\frac{ x+3 }{ x^2-25 }-\frac{ x-1 }{ x-5 }+\frac{ 3 }{x+3 }\]

Answer 2

I ended up with

\[\frac{ x^3+3x^2-x-51 }{ (x+3)(x+5)(x-5) }\]

Answer 3

the answer however says that the numerator is -x^3-3x^2-x-51 which i don't see what I did wrong

Answer 4

i also made the denominator the same for the first 2, subtracted them, then added the final term, so i didn't do all 3 at once

Answer 5

my problem may have came from
\[\frac{ x+3 }{ (x+5)(x-5) }-\frac{ (x-1)(x+5) }{ (x+5)(x-5) }\]

Answer 6

The numerator I got x^2-3x+8

Answer 7

\[\frac{ x+3 }{ x^2-25 }-\frac{ x-1 }{ x-5 }+\frac{ 3 }{x+3 }\]\[\frac{x+3\color{red}{(x+3)}}{(x+5)(x-5)\color{red}{(x+3)}} -\frac{x-1\color{red}{(x+5)(x+3)}}{(x-5)\color{red}{(x+5)(x+3)}} +\frac{3\color{red}{(x-5)(x+5)}}{(x+3)\color{red}{(x+5)(x-5)}}\]

Answer 8

\[\small (x+3)(x-5)(x+5)\left[ \frac{x+3\color{red}{(x+3)}}{(x+5)(x-5)\color{red}{(x+3)}} -\frac{x-1\color{red}{(x+5)(x+3)}}{(x-5)\color{red}{(x+5)(x+3)}} +\frac{3\color{red}{(x-5)(x+5)}}{(x+3)\color{red}{(x+5)(x-5)}}\right]\]

Answer 9

you end up with \[(x+3)(x+3) -[(x-1)(x+5)(x+3)] +3(x-5)(x+5)\]

Answer 10

then just solve.

Answer 11

Your numerator has an error in the sign for x^2 @dtan5457

Answer 12

i think i see my problem, the numerator is suppose to be -x^2, then, everything else works out

Answer 13

Combining the first two and then combining the last with your results should work.

Answer 14

yeah, that was the mistake i made, just the signs, everything else is clear, thanks.

Answer 15

Good luck with your studies.