Find the roots of quadratic equations 1/x + 1 + 2/x + 2 = 5/x + 4,x ≠ -1, -2, -4 ​

Question

Find the roots of quadratic equations \(\frac{1}{x+1}+\frac{2}{x+2}\) = \(\frac{5}{x+4}\),x ≠ -1, -2, -4

Answer 1

\(\frac{1}{x+1}+\frac{2}{x+2}\) = \(\frac{5}{x+4}\),x ≠ -1, -2, -4

⇒ \(\frac{x+2+2x+2}{(x+1)(x+2)}\) = \(\frac{5}{x+4}\)

⇒ \(\frac{3x+4}{x^2+3x+2}\) = \(\frac{5}{x+4}\)

Hence, 2 and - 3/2  are the roots of the given equation.