x3+9x22x\frac{x^3+9x^2}{2x} × x2−14x+45x2−81\frac{x^2-14x+45}{x^2-81}

asked by guest
on Nov 19, 2024 at 8:37 am



You asked:

Evaluate the expression: x3+9x22x⋅x2−14x+45x2−81\frac{{x}^{3} + 9 {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81}

MathBot Answer:

Evaluated



x3+9x22x⋅x2−14x+45x2−81=(x3+9x2)(x2−14x+45)2x(x2−81)\displaystyle \frac{{x}^{3} + 9 {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{\left(x^{3} + 9 x^{2}\right) \left(x^{2} - 14 x + 45\right)}{2 x \left(x^{2} - 81\right)}

Expanded

x3+9x22x⋅x2−14x+45x2−81=x42x2−162−5x32x2−162−81x22x2−162+405x2x2−162\frac{{x}^{3} + 9 {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{x^{4}}{2 x^{2} - 162} - \frac{5 x^{3}}{2 x^{2} - 162} - \frac{81 x^{2}}{2 x^{2} - 162} + \frac{405 x}{2 x^{2} - 162}

Factored

x3+9x22x⋅x2−14x+45x2−81=x(x−5)2\frac{{x}^{3} + 9 {x}^{2}}{2 x} \cdot \frac{{x}^{2} - 14 x + 45}{{x}^{2} - 81} = \frac{x \left(x - 5\right)}{2}

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