Solve (d-9+25/a+1)div(a-1-4a-1/a+1)

$$( d - 9 + \frac { 25 } { a + 1 } ) \div ( a - 1 - \frac { 4 a - 1 } { a + 1 } )$$

Evaluate

$$\frac{ad-9a+d+16}{a\left(a-4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply d-9 times \frac{a+1}{a+1}.

$$\frac{\frac{\left(d-9\right)\left(a+1\right)}{a+1}+\frac{25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Since \frac{\left(d-9\right)\left(a+1\right)}{a+1} and \frac{25}{a+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(d-9\right)\left(a+1\right)+25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Do the multiplications in \left(d-9\right)\left(a+1\right)+25.

$$\frac{\frac{da+d-9a-9+25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Combine like terms in da+d-9a-9+25.

$$\frac{\frac{da+d-9a+16}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

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

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{\left(a-1\right)\left(a+1\right)}{a+1}-\frac{4a-1}{a+1}}$$

Since \frac{\left(a-1\right)\left(a+1\right)}{a+1} and \frac{4a-1}{a+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{\left(a-1\right)\left(a+1\right)-\left(4a-1\right)}{a+1}}$$

Do the multiplications in \left(a-1\right)\left(a+1\right)-\left(4a-1\right).

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{a^{2}+a-a-1-4a+1}{a+1}}$$

Combine like terms in a^{2}+a-a-1-4a+1.

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{a^{2}-4a}{a+1}}$$

Divide \frac{da+d-9a+16}{a+1} by \frac{a^{2}-4a}{a+1} by multiplying \frac{da+d-9a+16}{a+1} by the reciprocal of \frac{a^{2}-4a}{a+1}.

$$\frac{\left(da+d-9a+16\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-4a\right)}$$

Cancel out a+1 in both numerator and denominator.

$$\frac{ad-9a+d+16}{a^{2}-4a}$$

Expand

$$\frac{ad-9a+d+16}{a^{2}-4a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply d-9 times \frac{a+1}{a+1}.

$$\frac{\frac{\left(d-9\right)\left(a+1\right)}{a+1}+\frac{25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Since \frac{\left(d-9\right)\left(a+1\right)}{a+1} and \frac{25}{a+1} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(d-9\right)\left(a+1\right)+25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Do the multiplications in \left(d-9\right)\left(a+1\right)+25.

$$\frac{\frac{da+d-9a-9+25}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

Combine like terms in da+d-9a-9+25.

$$\frac{\frac{da+d-9a+16}{a+1}}{a-1-\frac{4a-1}{a+1}}$$

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

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{\left(a-1\right)\left(a+1\right)}{a+1}-\frac{4a-1}{a+1}}$$

Since \frac{\left(a-1\right)\left(a+1\right)}{a+1} and \frac{4a-1}{a+1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{\left(a-1\right)\left(a+1\right)-\left(4a-1\right)}{a+1}}$$

Do the multiplications in \left(a-1\right)\left(a+1\right)-\left(4a-1\right).

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{a^{2}+a-a-1-4a+1}{a+1}}$$

Combine like terms in a^{2}+a-a-1-4a+1.

$$\frac{\frac{da+d-9a+16}{a+1}}{\frac{a^{2}-4a}{a+1}}$$

Divide \frac{da+d-9a+16}{a+1} by \frac{a^{2}-4a}{a+1} by multiplying \frac{da+d-9a+16}{a+1} by the reciprocal of \frac{a^{2}-4a}{a+1}.

$$\frac{\left(da+d-9a+16\right)\left(a+1\right)}{\left(a+1\right)\left(a^{2}-4a\right)}$$

Cancel out a+1 in both numerator and denominator.

$$\frac{ad-9a+d+16}{a^{2}-4a}$$