Question

Precal Help
a. Solve this rational equation:
2x+12/x-2=x/x-2+5 . Make sure Patricia will understand the LCM step well. Also spend some time discussing why identifying extraneous solutions is important.

Answer 1

Is this the correct equation? \[
\frac{2x+12}{x-2} = \frac{x}{x-2} + 5
\]

Answer 2

\[
2x + \frac{12}{x-2} = \frac{x}{x-2} + 5 = \\
\frac{2x}{1} + \frac{12}{x-2} = \frac{x}{x-2} + \frac 51 \\
\text{ } \\
\text{LCM of 1 and (x-2) in the denominator is (x-2)}. \\
\text{Multiply throughout by (x-2)}. \\
\text{ } \\
2x(x-2) + 12 = x + 5(x-2) \\
2x^2 - 4x + 12 = x + 5x - 10 \\
2x^2 - 4x + 12 = 6x - 10 \\
2x^2 - 4x + 12 - 6x + 10 = 0 \\
2x^2 - 10x + 22 = 0 \\
x^2 - 5x + 11 = 0
\]Solve the quadratic for x.

Answer 3

Thank you so much hun :)

Answer 4

You are welcome.