2/3ab^2-[(1/2a^2b)+(-3/4a^2b)-(+1/2a^2b)]+ab^2-3/2a^2b

asked by guest
on Jan 12, 2025 at 10:35 am



You asked:

Evaluate the expression: \(\frac{2}{3 a {b}^{2}} - \left(\frac{1}{2 {a}^{2} b} + \frac{-3}{4 {a}^{2} b} - \frac{1}{2 {a}^{2} b}\right) + a {b}^{2} - \frac{3}{2 {a}^{2} b}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{2}{3 a {b}^{2}} - \left(\frac{1}{2 {a}^{2} b} + \frac{-3}{4 {a}^{2} b} - \frac{1}{2 {a}^{2} b}\right) + a {b}^{2} - \frac{3}{2 {a}^{2} b} = b^{2} a + \frac{2}{3 b^{2} a} - \frac{3}{4 a^{2} b} \)

Expanded

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

Factored

\[\frac{2}{3 a {b}^{2}} - \left(\frac{1}{2 {a}^{2} b} + \frac{-3}{4 {a}^{2} b} - \frac{1}{2 {a}^{2} b}\right) + a {b}^{2} - \frac{3}{2 {a}^{2} b} = \frac{12 a^{3} b^{4} + 8 a - 9 b}{12 a^{2} b^{2}}\]

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