Question

Check my work someone, not sure if I'm going about this in the correct manner

Answer 1

Give me a second to type out the problem, thank you

Answer 2

Simplify the rational expression: \(\Large\frac{10^{2}+29x+21}{x^{2}-25}\times\frac{x+5}{2x+3}\)

Answer 3

So far, I've factored the top portion.

So \(10x^{2}+29x+21\) should turn into (5x+7)(2x+3)
while \(x^{2}-25\) should be (x-5)(x+5)

Answer 4

*factored both the numerator and denominator of the first part of the expression

Answer 5

So I tried cross-multiplying, but that brought me more complications...however, I noticed a few things

\(\huge\frac{(5x-7)(2x+3)}{(x-5)(x+5)}\times\frac{x+5}{2x+3}\)

\(\huge\frac{(5x-7)\color{red}{(2x+3)}}{(x-5)\color{red}{(x+5)}}\times\frac{\color{red}{x+5}}{\color{red}{2x+3}}\)


Can the things in red cancel out? And would that lead me with a final answer?

Answer 6

^This is where there are some clear holes in my recollection of simplifying. Someone clarify my thinking, thanks

Answer 7

you are correct. The `2x+3` terms will divide to 1 and effectively go away

since 1*(any number) = same number

the same applies to the `x+5` terms

Answer 8

so \(\huge\frac{5x+7}{x-5}\) would be final answer? I mean, I'm not sure if that could be simplified any further, but I don't think so.

Answer 9

that's as simplified as it gets

Answer 10

Hmm alright. Thank you for your time :)

Answer 11

you're welcome