algebra

Assuming this is $\frac{x}{x-7}=y$

Multiply both sides by x - 7:  $x = y(x-7)$

Distribute the y over the bracketed terms;   $x=yx-7y$

Subtract yx from both sides:  $x-yx=-7y$

Factor the left-hand side;  $x(1-y)=-7y$

Divide both sides by 1 - y:  $x=\frac{-7y}{1-y}$

Alternatively, we could write this as:  $x=\frac{7y}{y-1}$

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x/x - 7=y
(x-7x)/x = y
x - 7x = xy
x(1 - 7) = xy divide both sides by (1 - 7)
x =xy / (1 - 7)

x/(x-7) = y

x = y(x-7)

x = xy-7y

x-xy = -7y

xy-x = 7y

x(y-1) = 7y

x = 7y/(y-1)