what is x squared - 4 over x squared + 2x simplified

asked by guest
on Mar 31, 2025 at 12:35 pm



You asked:

Simplify the expression: x24x2+2x{x}^{2} - \frac{4}{{x}^{2}} + 2 x

MathBot Answer:

Simplified:

x24x2+2x=x3(x+2)4x2 {x}^{2} - \frac{4}{{x}^{2}} + 2 x = \frac{x^{3} \left(x + 2\right) - 4}{x^{2}}


x24x2+2x=x2+2x+4x2=x2x2x2+2xx2x24x2=x3(x+2)4x2\begin{aligned}x^{2} - \frac{4}{x^{2}} + 2 x&=x^{2} + 2 x + \frac{-4}{x^{2}}\\&=\frac{x^{2} x^{2}}{x^{2}} + \frac{2 x x^{2}}{x^{2}} - \frac{4}{x^{2}}\\&=\frac{x^{3} \left(x + 2\right) - 4}{x^{2}}\end{aligned}


Factored:

x24x2+2x=x4+2x34x2 {x}^{2} - \frac{4}{{x}^{2}} + 2 x = \frac{x^{4} + 2 x^{3} - 4}{x^{2}}