Here, we show you a step-by-step solved example of décomposition partielle des fractions. This solution was automatically generated by our smart calculator:
Factor the trinomial $x^2+2x-3$ finding two numbers that multiply to form $-3$ and added form $2$
Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values
Rewrite the fraction $\frac{1}{\left(x-1\right)\left(x+3\right)}$ 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 $\left(x-1\right)\left(x+3\right)$
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 fraction $\frac{1}{\left(x-1\right)\left(x+3\right)}$ in decomposed fractions equals
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