\(\frac{x-1}{2x+3}-\frac{3x+7}{2x-3}=\frac{10-4x^2}{4x^2-9}\)
\(\frac{x-1}{2x+3}-\frac{3x+7}{2x-3}=\frac{10-4x^2}{\left(2x-3\right)\left(2x+3\right)}\)
\(\frac{\left(x-1\right)\left(2x-3\right)}{\left(2x+3\right)\left(2x-3\right)}-\frac{\left(3x+7\right)\left(2x+3\right)}{\left(2x+3\right)\left(2x-3\right)}=\frac{10-4x^2}{\left(2x+3\right)\left(2x-3\right)}\)
2x2-3x-2x+3-(6x2+9x+14x+21)=10-4x2
2x2-3x-2x+3-6x2-9x-14x-21=10-4x2
2x2-3x-2x+3-6x2-9x-14x-21-10+4x2=0
2x2-6x2+4x2-3x-2x-9x-14x+3-21-10=0
-28x-28=0
-28x=28
x=28:(-28)
x=-1
\(\frac{x-1}{2x+3}-\frac{3x+7}{2x-3}=\frac{-4x^2+10}{4x^2-9}\)
\(\frac{x-1}{2x+3}-\frac{3x+7}{2x-3}=\frac{-2\left(2x^2-5\right)}{4x^2-9}\)
\(\frac{x-1}{2x+3}-\frac{3x+7}{2x-3}=\frac{-4x^2+10}{\left(2x+3\right)\left(2x-3\right)}\)
\(-4x^2-28x-18=-4x^2+10\)
\(-4x^2-28x-18+4x^2-10=0\)
\(-28x-28=0\)
\(-28x=28\)
\(x=-1\)
