$$\frac{32-15x+10x^{2}}{2x^{2}+17x-55}=\frac{2x+5}{2x-5}+\frac{4x-5}{x+11}$$
$x=-4$
$$32-15x+10x^{2}=\left(x+11\right)\left(2x+5\right)+\left(2x-5\right)\left(4x-5\right)$$
$$32-15x+10x^{2}=2x^{2}+27x+55+\left(2x-5\right)\left(4x-5\right)$$
$$32-15x+10x^{2}=2x^{2}+27x+55+8x^{2}-30x+25$$
$$32-15x+10x^{2}=10x^{2}+27x+55-30x+25$$
$$32-15x+10x^{2}=10x^{2}-3x+55+25$$
$$32-15x+10x^{2}=10x^{2}-3x+80$$
$$32-15x+10x^{2}-10x^{2}=-3x+80$$
$$32-15x=-3x+80$$
$$32-15x+3x=80$$
$$32-12x=80$$
$$-12x=80-32$$
$$-12x=48$$
$$x=\frac{48}{-12}$$
$$x=-4$$
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