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

Question

campbell_st · Answer

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

campbell_st · Answer

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