What is the answer to a(x+b)+b(x+a)=ab(a+b+2) ?

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

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a(x+b)+b(x+a)=ab(a+b+2)

a (x + b) + b (x + a) = ab (a + b + 2)

x = ab; a \neq = - b

Solution steps

a (x + b) + b (x + a) = ab (a + b + 2)

Expand

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

Expand

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

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

Move

2 ab

to the right side

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

Factor

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

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

Divide both sides by

a + b; a \neq = - b

x = ab; a \neq = - b

- 4 (y - 3) = 5 (2 y - 6)

\frac{x}{7} - 4 = \frac{x}{7}

x - 134 - 64 = - 484

15 = r - 6

x, 2 x - 5 y = 17

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