Question

Would you help me solve this rational function?
2x-5/x-3 -2 = 3/x+3

Answer 1

\[\frac{ 2x -5 }{ x-3 } -2 = \frac{ 3 }{ x+3 }\]

Answer 2

I know I need to find the Least common denominator but am not sure if it is (x-3) or (x+3) or both?

Answer 3

multiply x-3 to -2

Answer 4

then, once you get it into 2 terms, you can just cross multiply

Answer 5

@dtan5457 so my equation would then look like this:
\[\frac{ 2x-5 }{ -2x+6 }= \frac{ 3 }{ x+3 }\]
Correct?

Answer 6

\[\frac{ 2x-5 }{ x-3}-\frac{ -2x+6 }{ x-3 }=\frac{ 3 }{ x+3 }\]

Answer 7

now just subtract the like terms from the first two

Answer 8

\[\frac{ -2 }{ 1 }\times \frac{ x-3 }{ x-3 }=\frac{ -2x+6 }{ x-3 }\]

Answer 9

@dtan5457 When I subtracted like terms from the first two, 2x and -2x cancelled out, x-3 and x-3 cancelled out, I was left with -5 - +6?

Answer 10

common denominator. why would you change anything in the denominator when subtracting?

Answer 11

the top would simply be 2x-(-2x)

-5-6

Answer 12

Okay, I missed that. If you are subtracting and have a common denominator, why did you move the 2 common denominators into the other numerator and denominator?

Answer 13

you multiplied -2/1 by x-3 on both because if you don't multiply it onto both, then that changes the value of the fraction.