Question

Math equation

Answer 1

multiply both sides by x^2 + 1 and there will be lots of cancellations. Simplify and solve.

Answer 2

ok one second

Answer 3

$$
{x+5\over x^2 + x}={1\over x^2+x} - {x-6\over x+1}\\
\text{Multiply last term by x on top and bottom:}\\
{x+5\over x^2 + x}={1\over x^2+x} - {x(x-6)\over x (x+1)}\\
\text{Simplify:}\\
{x+5\over x^2 + x}={1\over x^2+x} - {x^2-6x\over x^2+x}\\
{x+5\over x^2 + x}={1-x^2+6x\over x^2+x} \\
{x+5\over x^2 + x}-\left ({1-x^2+6x\over x^2+x}\right )=0 \\
{x+5 -1+x^2-6x\over x^2+x}=0 \\
{x^2-5x+4\over x^2+x}=0 \\
{(x-1)(x-4)\over x^2+x}=0 \implies x=1\text{ and }x=4
$$
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