Question
$$xx-(x-1)\frac{x+2}{4x+1} = 5$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} xx-(x-1)\frac{x+2}{4x+1} &= 5&& \text{multiply ALL terms by } \color{blue}{ 4x+1 }. \\[1 em](4x+1)xx-(4x+1)(x-1)\frac{x+2}{4x+1} &= (4x+1)\cdot5&& \text{cancel out the denominators} \\[1 em]4x^3+x^2-(x^2+x-2) &= 20x+5&& \text{simplify left side} \\[1 em]4x^3+x^2-x^2-x+2 &= 20x+5&& \\[1 em]4x^3+x^2-x^2-x+2 &= 20x+5&& \\[1 em]4x^3-x+2 &= 20x+5&& \text{move all terms to the left hand side } \\[1 em]4x^3-x+2-20x-5 &= 0&& \text{simplify left side} \\[1 em]4x^3-21x-3 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver