Solve for a
a=\frac{8}{x+y}
x\neq -y
Solve for x
x=-y+\frac{8}{a}
a\neq 0
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\left(x+y\right)a=8
Combine all terms containing a.
\frac{\left(x+y\right)a}{x+y}=\frac{8}{x+y}
Divide both sides by x+y.
a=\frac{8}{x+y}
Dividing by x+y undoes the multiplication by x+y.
ax=8-ay
Subtract ay from both sides.
\frac{ax}{a}=\frac{8-ay}{a}
Divide both sides by a.
x=\frac{8-ay}{a}
Dividing by a undoes the multiplication by a.
x=-y+\frac{8}{a}
Divide 8-ay by a.
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