Solve f(g(x))=(x+1/x-2)^2+3 | Microsoft Math Solver

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\frac{\left(x+1\right)^{2}}{\left(x-2\right)^{2}}+3

To raise \frac{x+1}{x-2} to a power, raise both numerator and denominator to the power and then divide.

\frac{\left(x+1\right)^{2}}{\left(x-2\right)^{2}}+\frac{3\left(x-2\right)^{2}}{\left(x-2\right)^{2}}

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{2}}.

\frac{\left(x+1\right)^{2}+3\left(x-2\right)^{2}}{\left(x-2\right)^{2}}

Since \frac{\left(x+1\right)^{2}}{\left(x-2\right)^{2}} and \frac{3\left(x-2\right)^{2}}{\left(x-2\right)^{2}} have the same denominator, add them by adding their numerators.

\frac{x^{2}+2x+1+3x^{2}-12x+12}{\left(x-2\right)^{2}}

Do the multiplications in \left(x+1\right)^{2}+3\left(x-2\right)^{2}.

\frac{4x^{2}-10x+13}{\left(x-2\right)^{2}}

Combine like terms in x^{2}+2x+1+3x^{2}-12x+12.

\frac{4x^{2}-10x+13}{x^{2}-4x+4}

Expand \left(x-2\right)^{2}.