\(\Leftrightarrow\)\(\frac{\left(x+1\right)\left(x-7\right)}{\left(x-4\right)\left(x-7\right)}=\frac{\left(x+5\right)\left(x-4\right)}{\left(x-4\right)\left(x-7\right)}\)
\(\Rightarrow\)\(^{x^2-7x+x-7=x^2-4x+5x-20}\)
\(\Leftrightarrow\)\(x^2-x^2-6x-x-7+20=0\)
\(\Leftrightarrow-7x+13=0\)
\(\Leftrightarrow-7x=-13\)
\(\Rightarrow x=\frac{13}{7}\)
\(pt\Leftrightarrow\left(x+1\right)\left(x-7\right)=\left(x-4\right)\left(x+5\right)\)
\(\Leftrightarrow x^2-7x+x-7=x^2+5x-4x-20\)
\(\Leftrightarrow-7x=-13\Rightarrow x=\frac{13}{7}\)