Solve 1-1/b-42/b^2/1-frac{12{b}+35/b^2}

$$\frac { 1 - \frac { 1 } { b } - \frac { 42 } { b ^ { 2 } } } { 1 - \frac { 12 } { b } + \frac { 35 } { b ^ { 2 } } }$$

Evaluate

$$\frac{b+6}{b-5}$$

Short Solution Steps

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

$$\frac{\frac{b}{b}-\frac{1}{b}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

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

$$\frac{\frac{b-1}{b}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b^{2} is b^{2}. Multiply \frac{b-1}{b} times \frac{b}{b}.

$$\frac{\frac{\left(b-1\right)b}{b^{2}}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

Since \frac{\left(b-1\right)b}{b^{2}} and \frac{42}{b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(b-1\right)b-42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

Do the multiplications in \left(b-1\right)b-42.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

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

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b}{b}-\frac{12}{b}+\frac{35}{b^{2}}}$$

Since \frac{b}{b} and \frac{12}{b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b-12}{b}+\frac{35}{b^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b^{2} is b^{2}. Multiply \frac{b-12}{b} times \frac{b}{b}.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{\left(b-12\right)b}{b^{2}}+\frac{35}{b^{2}}}$$

Since \frac{\left(b-12\right)b}{b^{2}} and \frac{35}{b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{\left(b-12\right)b+35}{b^{2}}}$$

Do the multiplications in \left(b-12\right)b+35.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b^{2}-12b+35}{b^{2}}}$$

Divide \frac{b^{2}-b-42}{b^{2}} by \frac{b^{2}-12b+35}{b^{2}} by multiplying \frac{b^{2}-b-42}{b^{2}} by the reciprocal of \frac{b^{2}-12b+35}{b^{2}}.

$$\frac{\left(b^{2}-b-42\right)b^{2}}{b^{2}\left(b^{2}-12b+35\right)}$$

Cancel out b^{2} in both numerator and denominator.

$$\frac{b^{2}-b-42}{b^{2}-12b+35}$$

Factor the expressions that are not already factored.

$$\frac{\left(b-7\right)\left(b+6\right)}{\left(b-7\right)\left(b-5\right)}$$

Cancel out b-7 in both numerator and denominator.

$$\frac{b+6}{b-5}$$

Expand

$$\frac{b+6}{b-5}$$

Short Solution Steps

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

$$\frac{\frac{b}{b}-\frac{1}{b}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

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

$$\frac{\frac{b-1}{b}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b^{2} is b^{2}. Multiply \frac{b-1}{b} times \frac{b}{b}.

$$\frac{\frac{\left(b-1\right)b}{b^{2}}-\frac{42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

Since \frac{\left(b-1\right)b}{b^{2}} and \frac{42}{b^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(b-1\right)b-42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

Do the multiplications in \left(b-1\right)b-42.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{1-\frac{12}{b}+\frac{35}{b^{2}}}$$

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

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b}{b}-\frac{12}{b}+\frac{35}{b^{2}}}$$

Since \frac{b}{b} and \frac{12}{b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b-12}{b}+\frac{35}{b^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and b^{2} is b^{2}. Multiply \frac{b-12}{b} times \frac{b}{b}.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{\left(b-12\right)b}{b^{2}}+\frac{35}{b^{2}}}$$

Since \frac{\left(b-12\right)b}{b^{2}} and \frac{35}{b^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{\left(b-12\right)b+35}{b^{2}}}$$

Do the multiplications in \left(b-12\right)b+35.

$$\frac{\frac{b^{2}-b-42}{b^{2}}}{\frac{b^{2}-12b+35}{b^{2}}}$$

Divide \frac{b^{2}-b-42}{b^{2}} by \frac{b^{2}-12b+35}{b^{2}} by multiplying \frac{b^{2}-b-42}{b^{2}} by the reciprocal of \frac{b^{2}-12b+35}{b^{2}}.

$$\frac{\left(b^{2}-b-42\right)b^{2}}{b^{2}\left(b^{2}-12b+35\right)}$$

Cancel out b^{2} in both numerator and denominator.

$$\frac{b^{2}-b-42}{b^{2}-12b+35}$$

Factor the expressions that are not already factored.

$$\frac{\left(b-7\right)\left(b+6\right)}{\left(b-7\right)\left(b-5\right)}$$

Cancel out b-7 in both numerator and denominator.

$$\frac{b+6}{b-5}$$