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:  \(x=\frac{7y}{y-1}\)

.

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)