Question

What is the solution to the rational equation 4/3-2/x-5=6/3x-15

Answer 1

a) x = -8
b) x = -2
c) x=2
d) x=8

Answer 2

\[\frac{4}{3} - \frac{2}{(x - 5)} = \frac{6}{3x - 15}\]

Factor 3x - 15 to get:
\[\frac{4}{3} - \frac{2}{(x - 5)} = \frac{6}{3(x - 5)}\]

6\3 = 2 so

\[\frac{4}{3} - \frac{2}{(x - 5)} = \frac{2}{(x - 5)}\]

Add 2/(x - 5) to both sides:
\[\frac{4}{3} = \frac{2}{(x - 5)} + \frac{2}{(x - 5)}\]
\[\frac{4}{3} = \frac{4}{(x - 5)} \]

Divide both sides by 4; Multiply both sides by 3 to get:
\[\frac{4}{4} = \frac{3}{(x - 5)} \]
\[1 = \frac{3}{(x - 5)} \]

Multiply both sides by x - 5 to get
\[x - 5 = 3 \]

Finish it.

Answer 3

x=8