5/(8aˆ2-18bˆ2)+1/(2aˆ2+3ab)-1/(4ab-6bˆ2)

asked by guest
on Nov 26, 2024 at 7:15 am



You asked:

Evaluate the expression: \(\frac{5}{8 {a}^{2} - 18 {b}^{2}} + \frac{1}{2 {a}^{2} + 3 a b} - \frac{1}{4 a b - 6 {b}^{2}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{5}{8 {a}^{2} - 18 {b}^{2}} + \frac{1}{2 {a}^{2} + 3 a b} - \frac{1}{4 a b - 6 {b}^{2}} = - \frac{1}{4 a b - 6 b^{2}} + \frac{5}{8 a^{2} - 18 b^{2}} + \frac{1}{2 a^{2} + 3 a b} \)

Expanded

\[\frac{5}{8 {a}^{2} - 18 {b}^{2}} + \frac{1}{2 {a}^{2} + 3 a b} - \frac{1}{4 a b - 6 {b}^{2}} = - \frac{1}{4 a b - 6 b^{2}} + \frac{5}{8 a^{2} - 18 b^{2}} + \frac{1}{2 a^{2} + 3 a b}\]

Factored

\[\frac{5}{8 {a}^{2} - 18 {b}^{2}} + \frac{1}{2 {a}^{2} + 3 a b} - \frac{1}{4 a b - 6 {b}^{2}} = - \frac{a^{2} - 3 a b + 3 b^{2}}{a b \left(2 a - 3 b\right) \left(2 a + 3 b\right)}\]

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