What is the answer to (x+a)/a-(a^2+b^2}{ab}=\frac{x+b)/b-2 ?

The answer to (x+a)/a-(a^2+b^2}{ab}=\frac{x+b)/b-2 is x=b-a;\quad ab\ne 0,a\ne b

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

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

x = b - a; ab \neq = 0, a \neq = b

Solution steps

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

Multiply by LCM

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

Expand

a (x + b) : a x + ab

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

Add similar elements:

ab - 2 ab = - ab

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

Expand

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

b x + ab - a^{2} - b^{2} = a x - ab; ab \neq = 0

Move

ab

to the right side

b x - a^{2} - b^{2} = a x - 2 ab; ab \neq = 0

Move

a^{2}

to the right side

b x - b^{2} = a x - 2 ab + a^{2}; ab \neq = 0

Move

b^{2}

to the right side

b x = a x - 2 ab + a^{2} + b^{2}; ab \neq = 0

Move

a x

to the left side

b x - a x = - 2 ab + a^{2} + b^{2}; ab \neq = 0

Factor

b x - a x : x (b - a)

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

Divide both sides by

b - a; ab \neq = 0, a \neq = b

x = b - a; ab \neq = 0, a \neq = b

x, 4 x + 2 y = - 6

x, 7 x + 4 y = 28

3 x + 9 = 2 x + 5

4 (2 x - 6) = - 56

x, 7 x - y = - 3

What is the answer to (x+a)/a-(a^2+b^2}{ab}=\frac{x+b)/b-2 ?
The answer to (x+a)/a-(a^2+b^2}{ab}=\frac{x+b)/b-2 is x=b-a;\quad ab\ne 0,a\ne b