What is the answer to (ax+b)/(cx+d)=e ?

The answer to (ax+b)/(cx+d)=e is x=(ed-b)/(a-ec);\quad a\ne ec

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(ax+b)/(cx+d)=e

\frac{a x + b}{c x + d} = e

x = \frac{e d - b}{a - ec}; a \neq = ec

Solution steps

\frac{a x + b}{c x + d} = e

Multiply both sides by

c x + d

a x + b = e (c x + d)

Expand

e (c x + d) : ec x + e d

a x + b = ec x + e d

Move

b

to the right side

a x = ec x + e d - b

Move

ec x

to the left side

a x - ec x = e d - b

Factor

a x - ec x : x (a - ec)

x (a - ec) = e d - b

Divide both sides by

a - ec; a \neq = ec

x = \frac{e d - b}{a - ec}; a \neq = ec

\frac{a + 14}{a} = \frac{9 a}{a + 14}

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

\frac{1}{x + 2} - 3 = \frac{10}{x + 2}

\frac{45}{5 + y} = 13

x, y = \frac{x + 3}{2 x - 8}

What is the answer to (ax+b)/(cx+d)=e ?
The answer to (ax+b)/(cx+d)=e is x=(ed-b)/(a-ec);\quad a\ne ec