Question

solve 1 by x+1 +2 by x+2 = 4 by x+4 where x is not equal to -1,-2,-4.

Answer 1

1/ (x+1) + 2/(x+2) = 4/(x+4)
⇒1(x+2) + 2(x+1)/(x+1)(x+2) = 4/(x+4)
⇒x+2+2x+2/x²+3x+2 = 4/(x+4)
⇒3x+4/x²+3x+2 = 4/(x+4)
⇒(3x+4)(x+4) = 4(x²+3x+2)
⇒3x²+12x+4x+16 = 4x²+12x+8
⇒4x²-3x²+12x-12x-4x+8-16 = 0
⇒x²-4x-8 = 0
⇒(x)²-2(x)(2)+2²-2²-8=0
⇒(x-2)² = 4+8 = 12
⇒x-2=√12
⇒x = 2√3 + 2 or 2(√3+1)

Answer 2

Step by step solution is attached below