What is the answer to (a(x-a))/b =(b(x-b))/a ?

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

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(a(x-a))/b =(b(x-b))/a

\frac{a ( x - a )}{b} = \frac{b ( x - b )}{a}

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

Solution steps

\frac{a ( x - a )}{b} = \frac{b ( x - b )}{a}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

a (x - a) a = bb (x - b)

Simplify

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

Expand

a^{2} (x - a) : a^{2} x - a^{3}

Expand

b^{2} (x - b) : b^{2} x - b^{3}

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

Move

a^{3}

to the right side

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

Move

b^{2} x

to the left side

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

Factor

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

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

Divide both sides by

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

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

3 - y = - 4

7 x + 8 (6) = 41

\frac{3 x}{4} + \frac{2 x}{3} = 51

3 \frac{x}{2} + 2 \frac{x}{3} = 1 + 3 \frac{x}{2}

4 (3 x - 2) = 3 (2 x + 9)

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