What is the answer to (a+b)((a^2-b^2-ay)/(a-b))+by=2ab ?

The answer to (a+b)((a^2-b^2-ay)/(a-b))+by=2ab is y=a-b;\quad a-b\ne 0,a\ne ib,a\ne-ib

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(a+b)((a^2-b^2-ay)/(a-b))+by=2ab

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

y = a - b; a - b \neq = 0, a \neq = ib, a \neq = - ib

Solution steps

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

Expand

(a + b) (\frac{a ^{2} - b ^{2} - a y}{a - b}) + b y : \frac{a ^{3} + a ^{2} b - a b ^{2} - b ^{3} - a ^{2} y - b ^{2} y}{a - b}

\frac{a ^{3} + a ^{2} b - a b ^{2} - b ^{3} - a ^{2} y - b ^{2} y}{a - b} = 2 ab

Multiply both sides by

a - b

a^{3} + a^{2} b - a b^{2} - b^{3} - a^{2} y - b^{2} y = 2 ab (a - b); a - b \neq = 0

Expand

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

a^{3} + a^{2} b - a b^{2} - b^{3} - a^{2} y - b^{2} y = 2 a^{2} b - 2 a b^{2}; a - b \neq = 0

Move

a^{3}

to the right side

a^{2} b - a b^{2} - b^{3} - a^{2} y - b^{2} y = 2 a^{2} b - 2 a b^{2} - a^{3}; a - b \neq = 0

Move

a^{2} b

to the right side

- a b^{2} - b^{3} - a^{2} y - b^{2} y = - a^{3} + a^{2} b - 2 a b^{2}; a - b \neq = 0

Move

a b^{2}

to the right side

- b^{3} - a^{2} y - b^{2} y = - a^{3} + a^{2} b - a b^{2}; a - b \neq = 0

Move

b^{3}

to the right side

- a^{2} y - b^{2} y = - a^{3} + a^{2} b - a b^{2} + b^{3}; a - b \neq = 0

Factor

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

- y (a^{2} + b^{2}) = - a^{3} + a^{2} b - a b^{2} + b^{3}; a - b \neq = 0

Divide both sides by

- (a^{2} + b^{2}); a - b \neq = 0, a \neq = ib, a \neq = - ib

y = a - b; a - b \neq = 0, a \neq = ib, a \neq = - ib

x = 0.7 \cdot 1500 \cdot 1 \cdot 1 0^{- 6}

a = (x^{2} + x + 4) (x^{2} + x + 5) - (x^{2} + x + 3) (x^{2} + x + 6)

- 2 (3) + 20 (- 1) + 30 (2) = 53

- 2 (p - 3) = 5 (- 2 - 2 p)

\frac{x}{2} + 3 + x + 9 = 60

What is the answer to (a+b)((a^2-b^2-ay)/(a-b))+by=2ab ?
The answer to (a+b)((a^2-b^2-ay)/(a-b))+by=2ab is y=a-b;\quad a-b\ne 0,a\ne ib,a\ne-ib