#1**+2 **

\( \frac{x}{x}-5=\frac{4}{x}-4\)

We know that \(\frac{x}{x}\) is \(1\), therefore meaning that the left side of the equation is,

\(1-5=-4\)

Therefore our equation is now

\(-4=\frac{4}{x}-4\)

From there we can simplify by adding 4 to each side

\(0=\frac{4}{x}\)

There is no value of \(x\) that satisfies this equation.

Therefore there are no solutions

Ako180 Apr 5, 2020

#2**+2 **

As it was written by the Guest, ako correctly points out that this equation has no solutions. However, I will take it that they forgot parentheses(important!) around the denominator and numerator. I'll then solve it with this interpretation:

\({x\over x-5} = {4 \over x-4}\)

Cross multiplying ,we get

\(4x-20 = x^2-4x\)

Rearranging, we get:

\(x^2-8x + 20 = 0\)

Realizing that our roots are imaginary because of the discriminant(but the problem never limits the value of x, so I'll continue), we can use the quadratic formula to find:

\(x = {8 \pm \sqrt{-16} \over 2}\)

\(x = {8 \pm 4i \over 2} = 4\pm2i\)

jfan17 Apr 5, 2020