\frac{b + x}{b^2 + bx + x^2} - \frac{2x^3}{b^4 + b^2x^2 + x^4}.

asked by guest
on Jan 24, 2025 at 11:12 am



You asked:

Evaluate the expression: \(\frac{b + x}{{b}^{2} + b x + {x}^{2}} - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{b + x}{{b}^{2} + b x + {x}^{2}} - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = - \frac{2 x^{3}}{b^{4} + b^{2} x^{2} + x^{4}} + \frac{b + x}{b^{2} + b x + x^{2}} \)

Expanded

\[\frac{b + x}{{b}^{2} + b x + {x}^{2}} - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = \frac{b}{b^{2} + b x + x^{2}} - \frac{2 x^{3}}{b^{4} + b^{2} x^{2} + x^{4}} + \frac{x}{b^{2} + b x + x^{2}}\]

Factored

\[\frac{b + x}{{b}^{2} + b x + {x}^{2}} - \frac{2 {x}^{3}}{{b}^{4} + {b}^{2} {x}^{2} + {x}^{4}} = \frac{b - x}{b^{2} - b x + x^{2}}\]

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