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

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

Evaluate

$$r$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 3-1-a.

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

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

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

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

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

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

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

Combine like terms in 3-2+a.

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

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

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

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

$$1r$$

For any term t, t\times 1=t and 1t=t.

$$r$$

Differentiate w.r.t. r

$$1$$

Steps Using Definition of a Derivative

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

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

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

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

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

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

Combine like terms in 3-1-a.

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

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2-a}{1+a}\times \frac{3-2+a}{2-a}r)$$

Combine like terms in 3-2+a.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2-a}{1+a}\times \frac{1+a}{2-a}r)$$

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(1r)$$

The derivative of ax^{n} is nax^{n-1}.

$$r^{1-1}$$

Subtract 1 from 1.

$$r^{0}$$

For any term t except 0, t^{0}=1.

$$1$$