Here, we show you a step-by-step solved example of partial fraction decomposition. This solution was automatically generated by our smart calculator:
Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
Calculate the power $\sqrt{4}$
Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
Calculate the power $\sqrt{4}$
Multiply $-1$ times $2$
Rewrite the fraction $\frac{x-1}{\left(x+2\right)\left(x-2\right)}$ in $2$ simpler fractions using partial fraction decomposition
Find the values for the unknown coefficients: $A, B$. The first step is to multiply both sides of the equation from the previous step by $\left(x+2\right)\left(x-2\right)$
Multiplying polynomials
Simplifying
Assigning values to $x$ we obtain the following system of equations
Proceed to solve the system of linear equations
Rewrite as a coefficient matrix
Reducing the original matrix to a identity matrix using Gaussian Elimination
The integral of $\frac{x-1}{\left(x+2\right)\left(x-2\right)}$ in decomposed fraction equals
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