If a = x/(x+y) and b = y/(x-y) , then ab/(a+b) is equal to

Question

If \(a=\frac{x}{x+y} \,\text{and}\,b=\frac{y}{x-y}\,\text{then}\,\frac{ab}{a+b}\) is equal to

(a) \(\frac{xy}{x^2+y^2}\)

(b) \(\frac{x^2+y^2}{xy}\)

(c) \(\frac{x}{x+y}\)

(d) \(\big(\frac{y}{x+y}\big)^2\)

Answer 1

(a) \(\frac{xy}{x^2+y^2}\)

ab = \(\big(\frac{x}{x+y}\big) \times\big(\frac{y}{x-y}\big)\)