## anonymous 4 years ago how would you solve 4x^2-9/x^2-11x-60 multiplied by x^2-16/2x+3

1. Mertsj

$\frac{4x^2-9}{x^2-11x-60} \times \frac{x^2-16}{2x+3}$

2. Mertsj

$\frac{(2x-3)(2x+3)}{(x-15)(x+4)} \times \frac{(x-4)(x+4)}{2x+3}$

3. ash2326

$\frac{4x^2-9}{x^2-11x-60} *\frac{x^2-16}{2x+3}$ let's factor we know $a^2-b^2=(a+b)(a-b)$ so we have now $\frac{(2x-3)(2x+3)}{x^2-11x-60} *\frac{(x-4)(x+4)}{2x+3}$ let's factor x^2-11x-60 let's find factor of -60 , whose sum is -11 -15 and 4 x^2-15x+4x-60 (x-15)(x+4) now let's rewrite thr polynomial fraction given $\frac{(2x-3)(2x+3)}{(x-15)(x+4)} *\frac{(x-4)(x+4)}{2x+3}$ let's cancel the common terms $\frac{(2x-3)\cancel{(2x+3)}}{(x-15)\cancel {(x+4)}} *\frac{(x-4)\cancel{(x+4)}}{\cancel{2x+3}}$ we get finally $\frac{(2x-3)(x-4)}{x-15}$

4. Mertsj

$\frac{(2x-3)(x-4)}{x-15}$

5. anonymous

oh ok i forgot to factor the 4x^2-9. Thank you very much!

6. anonymous

would the answer for 5x/x^2-7x+10 minus 4/x^2-25 be 5x-4/x-5?

7. anonymous

|dw:1328738038677:dw|

8. anonymous

complex fraction

9. ash2326

$\frac { \frac{1}{x}-\frac{1}{(x+1)}}{x-1}$ LCM of x and x+1 is x(x+1) $\frac { \frac{x+1}{x(x+1)}-\frac{x}{x(x+1)}}{x-1}$ we get now $\frac { \frac{1}{x(x+1)}}{x-1}$ we get finally $\frac 1 {{(x)(x+1)}(x-1)}$

10. anonymous

what happened to the 2?

11. Mertsj

|dw:1328738538884:dw|

12. Mertsj

Final answer: $\frac{-1}{x(x+1)}$

13. anonymous

oh ok now isee it Thanks again you guys have been a great help

14. anonymous

this is all part of this welcome back worksheet in pre cal and i'm not really good with complex fractions. I still have sin,cos,tan on my mind lol

15. anonymous

|dw:1328739265241:dw|

16. anonymous

Rationalizing the denominator