​ Solve the following systems of equations: 5/(x+1) - 2/(y - 1) = 1/2 10/(x+1) + 2/(y - 1) = 5/2 where, x ≠ -1, y ≠ 1 ​

Question

Solve the following systems of equations:

\(\frac{5}{x+1}\) - \(\frac{2}{y-1}\) = \(\frac{1}{2}\)

\(\frac{10}{x+1}\) + \(\frac{2}{y-1}\) = \(\frac{5}{2}\)

where, x ≠ -1, y ≠ 1

Answer 1

 \(\frac{5}{x+1}\) - \(\frac{2}{y-1}\) = \(\frac{1}{2}\)

\(\frac{10}{x+1}\) + \(\frac{2}{y-1}\) = \(\frac{5}{2}\)

Adding eq1 and eq2

⇒ 15/(x + 1) = 3

⇒ x + 1 = 5

⇒ x = 4

Thus,

5/5 – 2/(y – 1) = 12

⇒ y – 1 = 4

⇒ y = 5