What is the answer to b/(ax-1)-a/(bx-1)=0 ?

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

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b/(ax-1)-a/(bx-1)=0

\frac{b}{a x - 1} - \frac{a}{b x - 1} = 0

x = \frac{1}{b + a}; b \neq = a, b \neq = - a

Solution steps

\frac{b}{a x - 1} - \frac{a}{b x - 1} = 0

Multiply by LCM

b (b x - 1) - a (a x - 1) = 0

Expand

b (b x - 1) : b^{2} x - b

b^{2} x - b - a (a x - 1) = 0

Expand

- a (a x - 1) : - a^{2} x + a

b^{2} x - b - a^{2} x + a = 0

Move

b

to the right side

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

Move

a

to the right side

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

Factor

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

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

Divide both sides by

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

x = \frac{1}{b + a}; b \neq = a, b \neq = - a

6 (1 - x^{2})^{- 1} + 3 (1 - x)^{- 1} = 5 (x + 1)^{- 1}

\frac{3}{5} + \frac{7}{6 x} = \frac{1}{8 x}

\frac{1}{x} = \frac{2}{5 x} - \frac{6}{5}

x = \frac{25}{x}

\frac{a - x}{a + x}

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