JAMB - Mathematics (1990 - No. 22)
Simplify \(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)
\(\frac{x}{x^2 - y^2}\)
\(\frac{y^2}{x^2 - y^2}\)
\(\frac{x^2}{x^2 - y^2}\)
\(\frac{y}{x^2 - y^2}\)
Wyjaśnienie
\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{x^2 - y^2}\)
\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{(x + y)(x - y}\)
= \(\frac{x(x - y) + y(x + y) - x^2}{(x + y)(x - y}\)
= \(\frac{x^2 + xy + xy + y^2 - x^2}{(x + y)(x - y}\)
= \(\frac{y^2}{(x + y)(x - y)}\)
= \(\frac{y^2}{(x^2 - y^2)}\)
\(\frac{x}{x + y}\) + \(\frac{y}{x - y}\) - \(\frac{x^2}{(x + y)(x - y}\)
= \(\frac{x(x - y) + y(x + y) - x^2}{(x + y)(x - y}\)
= \(\frac{x^2 + xy + xy + y^2 - x^2}{(x + y)(x - y}\)
= \(\frac{y^2}{(x + y)(x - y)}\)
= \(\frac{y^2}{(x^2 - y^2)}\)