Solve for t (complex solution)
t=\frac{x^{2}+\sqrt{x+1}}{x+1}
x\neq -1
Solve for t
t=\frac{x^{2}+\sqrt{x+1}}{x+1}
x>-1
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x^{2}-tx+\sqrt{x+1}-t=0
Subtract t from both sides.
-tx+\sqrt{x+1}-t=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
-tx-t=-x^{2}-\sqrt{x+1}
Subtract \sqrt{x+1} from both sides.
\left(-x-1\right)t=-x^{2}-\sqrt{x+1}
Combine all terms containing t.
\frac{\left(-x-1\right)t}{-x-1}=\frac{-x^{2}-\sqrt{x+1}}{-x-1}
Divide both sides by -x-1.
t=\frac{-x^{2}-\sqrt{x+1}}{-x-1}
Dividing by -x-1 undoes the multiplication by -x-1.
t=\frac{x^{2}+\sqrt{x+1}}{x+1}
Divide -x^{2}-\sqrt{x+1} by -x-1.
x^{2}-tx+\sqrt{x+1}-t=0
Subtract t from both sides.
-tx+\sqrt{x+1}-t=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
-tx-t=-x^{2}-\sqrt{x+1}
Subtract \sqrt{x+1} from both sides.
\left(-x-1\right)t=-x^{2}-\sqrt{x+1}
Combine all terms containing t.
\frac{\left(-x-1\right)t}{-x-1}=\frac{-x^{2}-\sqrt{x+1}}{-x-1}
Divide both sides by -x-1.
t=\frac{-x^{2}-\sqrt{x+1}}{-x-1}
Dividing by -x-1 undoes the multiplication by -x-1.
t=\frac{x^{2}+\sqrt{x+1}}{x+1}
Divide -x^{2}-\sqrt{x+1} by -x-1.
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