Question

 

Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3

 

Answer 1

`1/(x+1)+2/(x+2)=4/(x+4)`

L.C.M. of all the denominators is (x + 1)(x + 2)(x + 4)

Multiply throughout by the L.C.M.,we get

(x + 2)(x + 4) + 2(x + 1)(x + 4) = 4(x + 1)(x + 2)

∴ (x + 4)(x + 2 + 2x + 2) = 4(x² + 3x + 2)

∴ (x + 4)(3x + 4) 4x² + 12x + 8

∴ 3x² + 16x + 16 = 4x² + 12 x 8

∴ x²-4x-8=0

Now,a = 1,b = -4,c = -8

`x=(-b+-sqrt(b^2-4ac))/(2a)=(4+-sqrt(16+32))/2=(4+-sqrt48)/2=(4+-4sqrt3)/2`

`:.x=2+-2sqrt3`