Solve (3/1+beta-1)*(3/2-beta-1)

$$( \frac { 3 } { 1 + \beta } - 1 ) \cdot ( \frac { 3 } { 2 - \beta } - 1 )$$

Evaluate

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Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1+\beta }{1+\beta }.

$$\left(\frac{3}{1+\beta }-\frac{1+\beta }{1+\beta }\right)\left(\frac{3}{2-\beta }-1\right)$$

Since \frac{3}{1+\beta } and \frac{1+\beta }{1+\beta } have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-\left(1+\beta \right)}{1+\beta }\left(\frac{3}{2-\beta }-1\right)$$

Do the multiplications in 3-\left(1+\beta \right).

$$\frac{3-1-\beta }{1+\beta }\left(\frac{3}{2-\beta }-1\right)$$

Combine like terms in 3-1-\beta .

$$\frac{2-\beta }{1+\beta }\left(\frac{3}{2-\beta }-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2-\beta }{2-\beta }.

$$\frac{2-\beta }{1+\beta }\left(\frac{3}{2-\beta }-\frac{2-\beta }{2-\beta }\right)$$

Since \frac{3}{2-\beta } and \frac{2-\beta }{2-\beta } have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\beta }{1+\beta }\times \frac{3-\left(2-\beta \right)}{2-\beta }$$

Do the multiplications in 3-\left(2-\beta \right).

$$\frac{2-\beta }{1+\beta }\times \frac{3-2+\beta }{2-\beta }$$

Combine like terms in 3-2+\beta .

$$\frac{2-\beta }{1+\beta }\times \frac{1+\beta }{2-\beta }$$

Multiply \frac{2-\beta }{1+\beta } times \frac{1+\beta }{2-\beta } by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2-\beta \right)\left(1+\beta \right)}{\left(1+\beta \right)\left(2-\beta \right)}$$

Cancel out \left(\beta +1\right)\left(-\beta +2\right) in both numerator and denominator.

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Factor

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