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

The answer to x-a= a/b (x-b) is x=0;\quad b\ne 0

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

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

x = 0; b \neq = 0

Solution steps

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

Expand

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

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

Move

a

to the right side

x = \frac{a x}{b}

Multiply both sides by

b

x b = a x; b \neq = 0

Move

a x

to the left side

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

Factor

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

x (b - a) = 0; b \neq = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0; b \neq = 0

- 4 + x = - 27

9 R - 55 = - 9 R + 53

3 = \frac{x}{9}

y, y + 2 = x

x, 9 x - 3 y = 81

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