What is (a^2-b^2)/(2a+2b) ?

The solution to (a^2-b^2)/(2a+2b) is (a-b)/2

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simplify (a^2-b^2)/(2a+2b)

simplify

\frac{a ^{2} - b ^{2}}{2 a + 2 b}

\frac{a - b}{2}

Solution steps

\frac{a ^{2} - b ^{2}}{2 a + 2 b}

Apply Difference of Two Squares Formula:

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

a^{2} - b^{2} = (a + b) (a - b)

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

Factor out common term

2

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

Cancel the common factor:

a + b

= \frac{a - b}{2}

x + 1 = x

2 < 3 a < 8

4 x^{2} + 4 x + 4

\frac{5 x + 3 y}{2 x ^{2} y} - \frac{3 x + 4 y}{x y ^{2}}

16 t^{2} + 80 t + 32 = 0