What is the answer to a/b =((2x))/((x-4)) ?

The answer to a/b =((2x))/((x-4)) is x=(4a)/(a-2b);\quad b\ne 0,a\ne 2b

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a/b =((2x))/((x-4))

\frac{a}{b} = \frac{( 2 x )}{( x - 4 )}

x = \frac{4 a}{a - 2 b}; b \neq = 0, a \neq = 2 b

Solution steps

\frac{a}{b} = \frac{( 2 x )}{( x - 4 )}

Cross multiply

a x - 4 a = b \cdot 2 x

Move

4 a

to the right side

a x = b \cdot 2 x + 4 a

Move

b 2 x

to the left side

a x - b \cdot 2 x = 4 a

Factor

a x - b \cdot 2 x : x (a - 2 b)

x (a - 2 b) = 4 a

Divide both sides by

a - 2 b; a \neq = 2 b

x = \frac{4 a}{a - 2 b}; b \neq = 0, a \neq = 2 b

\frac{n !}{( n - 2 ) !} = 30

\frac{x + 1}{2 x + 3} = \frac{3}{8}

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

\frac{( x + 5 ) !}{( x + 4 ) !} = 9

\frac{3}{2 x} = \frac{1}{12}

What is the answer to a/b =((2x))/((x-4)) ?
The answer to a/b =((2x))/((x-4)) is x=(4a)/(a-2b);\quad b\ne 0,a\ne 2b