What is (x^2-y^2)/(x^2+xy) ?

The solution to (x^2-y^2)/(x^2+xy) is (x-y)/x

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simplify (x^2-y^2)/(x^2+xy)

simplify

\frac{x ^{2} - y ^{2}}{x ^{2} + x y}

\frac{x - y}{x}

Solution steps

\frac{x ^{2} - y ^{2}}{x ^{2} + x y}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

x^{2} - y^{2} = (x + y) (x - y)

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

Factor

x^{2} + x y : x (x + y)

= \frac{( x + y ) ( x - y )}{x ( x + y )}

Cancel the common factor:

x + y

= \frac{x - y}{x}

(x - 1) 3

\frac{x - 5}{x ^{2} - 10 x + 25}

\frac{2}{5} \div \frac{1}{3}

\frac{9 x}{8} - \frac{3}{7}

\frac{2}{3} \cdot (- 2)