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

The answer to (x+a)/x =(b+ba)/b is x=1;\quad b\ne 0,a\ne 0

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(x+a)/x =(b+ba)/b

\frac{x + a}{x} = \frac{b + ba}{b}

x = 1; b \neq = 0, a \neq = 0

Solution steps

\frac{x + a}{x} = \frac{b + ba}{b}

Cross multiply

b x + ab = b x + ab x

Move

ab

to the right side

b x = b x + ab x - ab

Subtract

b x + ab x

from both sides

b x - (b x + ab x) = b x + ab x - ab - (b x + ab x)

Simplify

- ab x = - ab

Divide both sides by

- ab; a \neq = 0

x = 1; b \neq = 0, a \neq = 0

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 1; b \neq = 0, a \neq = 0

y, x = \frac{1 + y}{1 - y}

x^{- 2} + 9 x^{- 1} + 20 = 0

\frac{6}{x ^{4}} = 0

\frac{8}{x ^{2}} = \frac{32}{36}

\frac{3 x - 7}{3 x + 9} = \frac{5}{6}

What is the answer to (x+a)/x =(b+ba)/b ?
The answer to (x+a)/x =(b+ba)/b is x=1;\quad b\ne 0,a\ne 0