What is (ax-ay-2by+2bx)/(ax+2bx+2by+ay) ?

The solution to (ax-ay-2by+2bx)/(ax+2bx+2by+ay) is (x-y)/(x+y)

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simplify (ax-ay-2by+2bx)/(ax+2bx+2by+ay)

simplify

\frac{a x - a y - 2 b y + 2 b x}{a x + 2 b x + 2 b y + a y}

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

Solution steps

\frac{a x - a y - 2 b y + 2 b x}{a x + 2 b x + 2 b y + a y}

Factor

a x - a y - 2 b y + 2 b x : (x - y) (a + 2 b)

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

Factor

a x + 2 b x + 2 b y + a y : (x + y) (a + 2 b)

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

Cancel the common factor:

a + 2 b

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

\frac{4}{b - 4} + \frac{b}{b - 4}

3 y^{7} 75

3 x + \frac{3}{x - 4}

\frac{6}{1 - 3}

- 12 - (- 2)

What is (ax-ay-2by+2bx)/(ax+2bx+2by+ay) ?
The solution to (ax-ay-2by+2bx)/(ax+2bx+2by+ay) is (x-y)/(x+y)