Solve for x: 5 over quantity x squared minus 1 minus 2 over x equals 2 over quantity x plus 1

Question

campbell_st · Answer

is this your equation

$$\frac{5}{x^2 -1} - \frac{2}{x} = \frac{2}{x+1}$$

anonymous · Answer

yes

campbell_st · Answer

ok...get rid of the denominators by multiplying every term by   x(x^2 -1)

$$\frac{ 5\times x(x^2 -1)}{x^2 -1} - \frac{2\times  x(x^2 -1)}{x} = \frac{2\times x(x^2-1)}{x+1}$$

this is a little long.. sorry... but the right hand side can be simplified 
because x^2 -1 = (x+1)(x-1)

so you end up with 

$$5x -2(x^2 -1) = 2x(x-1)$$

simplify and collect like terms

$$4x^2 -7x - 2 = 0$$

campbell_st · Answer

this factorises to 

(x - 2)(4x + 1) = 0

then x = 2 or - 1/4