Question

Rational Functions: 4/6-x + x^2/6-x = 2

Answer 1

Might help to write it symbolically:\[\frac{4}{6-x}+\frac{x^2}{6-x}=2\] \[\frac{4+x^2}{6-x}=2\]
\[4+x^2=12-2x\]
\[x^2+2x-8=0\]

\[(x+4)(x-2)=0\]

x = -4 or x = 2. Tell me if any part of that was confusing.

Answer 2

Nope, I get it I had a feeling that was the answer just wanted to double check. Thank You

Answer 3

Great, you're welcome.

Answer 4

Can you help me with one more?

Answer 5

Sure

Answer 6

ok one sec

Answer 7

1/x^2-7x+10 = x/x-5+1/x-2

Answer 8

\[\frac{1}{x^2-7x+10} = \frac{x}{x-5}+\frac{1}{x-2}\]
\[\frac{1}{x^2-7x+10} = \frac{x^2-x-5}{x^2-7x+10}\]

\[0= \frac{x^2-x-6}{x^2-7x+10}\]
\[x^2-x-6 = 0\]
x = 3 or -2. But you have to plug back in to see if there's any problems - turns out, there aren't. Those are the solutions.

Answer 9

Sweet! Thank You again. Happy Holidays

Answer 10

Happy Holidays!