SOLUTION: I need help solving/factoring this rational equation: {(7x+1)/(2x+5)} +1 = {(10x-3)/3x} I was able to get it to 7x2 - 26x + 15 = 0 but from there I'm unable to factor to solv

Algebra ->  Rational-functions -> SOLUTION: I need help solving/factoring this rational equation: {(7x+1)/(2x+5)} +1 = {(10x-3)/3x} I was able to get it to 7x2 - 26x + 15 = 0 but from there I'm unable to factor to solv      Log On


   

Question 383392: I need help solving/factoring this rational equation:
{(7x+1)/(2x+5)} +1 = {(10x-3)/3x}
I was able to get it to 7x2 - 26x + 15 = 0 but from there I'm unable to factor to solve for x.
Thank you!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a common denominator, 3x%282x%2B5%29
%287x%2B1%29%2F%282x%2B5%29=%28%287x%2B1%29%283x%29%29%2F%283x%282x%2B5%29%29
1=%28%283x%29%282x%2B5%29%29%2F%283x%282x%2B5%29%29
%2810x-3%29%2F%283x%29=%28%2810x-3%29%282x%2B5%29%29%2F%283x%282x%2B5%29%29
So then,
%28%287x%2B1%29%2F%282x%2B5%29%29+%2B1+=+%28%2810x-3%29%2F3x%29




%28%2821x%5E2%2B6x%5E2-20x%5E2%29%2B%283x%2B15x-44x%29%2B15%29%2F%283x%282x%2B5%29%29=0
%287x%5E2-26x%2B15%29%2F%283x%282x%2B5%29%29=0
%28%287x-5%29%28x-3%29%29%2F%283x%282x%2B5%29%29=0
The left hand side equals zero where the numerator equals zero.
%287x-5%29%28x-3%29=0
Two solutions:
7x-5=0
7x=5
highlight%28x=5%2F7%29
.
.
.
x-3=0
highlight%28x=3%29