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

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

Evaluate

$$1$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 3-1-a.

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

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

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

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

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

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

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

Combine like terms in 3-2+a.

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

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

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

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

$$1$$

Factor

$$1$$