SOLUTION: Simplify: {{{ (7x - 9) / (x^2 - 25) }}} - {{{ 3 / (x - 5) }}} = {{{ 2 / (x - 5) }}}

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Question 143103: Simplify: +%287x+-+9%29+%2F++%28x%5E2+-+25%29+ - +3+%2F+%28x+-+5%29+ = +2+%2F+%28x+-+5%29+
Found 2 solutions by checkley77, ptaylor:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(7x-9)/(x^2-25)-3/(x-5)=2/(x-5)
(7x-9)/x^2-25)=3/(x-5)+2/(x-5)
(7x-9)/(x-5)(x+5)=5/(x-5) now cancel out the (x-5) terms in the denominators.
(7x-9)/(x+5)=5 now cross multiply.
7x-9=5(x+5)
7x-9=5x+25
7x-5x=25+9
2x=34
x=34/2
x=17 answer.
Proof:
(7*17-9)/(17^2-25)-3/(17-5)=2/(17-5)
(119-9)/(289-25)-3/(17-5)=2/917-5)
110/264-3/12=2/12
5/12-3/12=2/12
2/12=2/12

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:+%287x+-+9%29+%2F++%28x%5E2+-+25%29+ - +3+%2F+%28x+-+5%29+ = +2+%2F+%28x+-+5%29+
First, we need to recognize that %28x%5E2-25%29=%28x-5%29%28x%2B5%29
So, x%5E2-25 is the LCM and we need to multiply each term by x%5E2-25%29. When we do, we get:
%287x-9%29-3%28x%2B5%29=2%28x%2B5%29 get rid of parens
7x-9-3x-15=2x%2B10 or
4x-24=2x%2B10 add 24 to and subtract 2x from each side:
4x-24%2B24-2x=2x-2x%2B24%2B10 collect like terms
2x=34 divide each side by 2
x=17----------------------------------ans

Hope this helps---ptaylor