How do I find a coordinate when I know the two lines that go through it?

Question

One line is $y=4x-3$ and the other is $f(x)=\frac{x^2}{(x-2)^2}$ and I just need to find the coordinate that the lines both cut through. I thought I could make an equation out of the two equations so that $f(x)=y$ but it didn't work out too well.

Answer 1

$$f(x)=\frac{x^2}{(x-2)^2}$$ is not a line, you must solve the equation $$4x-3=\frac{x^2}{(x-2)^2}$$ for $x$ factorizing the term $$4x-3-\frac{x^2}{(x-2)^2}$$ we get $$4\,{\frac { \left( x-3 \right) \left( x-1 \right) ^{2}}{ \left( x-2 \right) ^{2}}} $$