+34 \( \frac{x}{x}-5=\frac{4}{x}-4\)
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
+499 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:
\(x = {8 \pm \sqrt{-16} \over 2}\)
\(x = {8 \pm 4i \over 2} = 4\pm2i\)
