What is the answer to solvefor x,(x+a)^2-(x-b)^2=2a(a-b) ?

The answer to solvefor x,(x+a)^2-(x-b)^2=2a(a-b) is x=(a^2-2ab+b^2)/(2(a+b));\quad a\ne-b

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solvefor x,(x+a)^2-(x-b)^2=2a(a-b)

solve for

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

x = \frac{a ^{2} - 2 ab + b ^{2}}{2 ( a + b )}; a \neq = - b

Solution steps

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

Expand

(x + a)^{2} - (x - b)^{2} : 2 a x + 2 b x + a^{2} - b^{2}

Expand

2 a (a - b) : 2 a^{2} - 2 ab

2 a x + 2 b x + a^{2} - b^{2} = 2 a^{2} - 2 ab

Move

a^{2}

to the right side

2 a x + 2 b x - b^{2} = a^{2} - 2 ab

Move

b^{2}

to the right side

2 a x + 2 b x = a^{2} - 2 ab + b^{2}

Factor

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

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

Divide both sides by

2 (a + b); a \neq = - b

x = \frac{a ^{2} - 2 ab + b ^{2}}{2 ( a + b )}; a \neq = - b

\frac{x - 5}{3} = \frac{x}{5} - \frac{1}{15}

\frac{1}{4} (2 - x) + \frac{3}{2} = 3 (x - 2)

x, y + 2 = - 2 (x + 4)

x, y - 2 = 4 (x + 1)

3 (4 - 5 x) - 10 x = - 28 x + 7

What is the answer to solvefor x,(x+a)^2-(x-b)^2=2a(a-b) ?
The answer to solvefor x,(x+a)^2-(x-b)^2=2a(a-b) is x=(a^2-2ab+b^2)/(2(a+b));\quad a\ne-b