Question

What is the solution to the rational equation x over x squared minus 9 minus 1 over x minus 3 equals 1 over 4x minus 12 ? @midhun.madhu1987

Answer 1

so the equation looks like

\[\frac{x}{x^2 - 9} + \frac{1}{x -3} = \frac{1}{4x - 12}\]

factor the denominator of the 1st fraction and the last and you get

\[\frac{x}{(x + 3)(x -3)} + \frac{1}{(x -3)} = \frac {1}{4(x - 3)}\]

Answer 2

next multiply every fraction by (x - 3)

and you get

\[\frac{x}{x + 3} + 1 = \frac{1}{4}\]

subtract 1 from both sides

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

cross multiply then which gives

\[4x = -3(x + 3)\]

now solve for x