Solve -1/1+12y*(1+3y)(1+61)/10

$$- \frac { 1 } { 1 + 12 y } \cdot \frac { ( 1 + 3 y ) ( 1 + 61 ) } { 10 }$$

Evaluate

$$-\frac{31\left(3y+1\right)}{5\left(12y+1\right)}$$

Short Solution Steps

Add 1 and 61 to get 62.

$$\left(-\frac{1}{1+12y}\right)\times \frac{\left(1+3y\right)\times 62}{10}$$

Divide \left(1+3y\right)\times 62 by 10 to get \left(1+3y\right)\times \frac{31}{5}.

$$\left(-\frac{1}{1+12y}\right)\left(1+3y\right)\times \frac{31}{5}$$

Use the distributive property to multiply 1+3y by \frac{31}{5}.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+3y\times \frac{31}{5}\right)$$

Express 3\times \frac{31}{5} as a single fraction.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+\frac{3\times 31}{5}y\right)$$

Multiply 3 and 31 to get 93.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+\frac{93}{5}y\right)$$

Use the distributive property to multiply -\frac{1}{1+12y} by \frac{31}{5}+\frac{93}{5}y.

$$\left(-\frac{1}{1+12y}\right)\times \frac{31}{5}+\left(-\frac{1}{1+12y}\right)\times \frac{93}{5}y$$

Multiply -\frac{1}{1+12y} times \frac{31}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31}{\left(1+12y\right)\times 5}+\left(-\frac{1}{1+12y}\right)\times \frac{93}{5}y$$

Multiply -\frac{1}{1+12y} times \frac{93}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31}{\left(1+12y\right)\times 5}+\frac{-93}{\left(1+12y\right)\times 5}y$$

Express \frac{-93}{\left(1+12y\right)\times 5}y as a single fraction.

$$\frac{-31}{\left(1+12y\right)\times 5}+\frac{-93y}{\left(1+12y\right)\times 5}$$

Since \frac{-31}{\left(1+12y\right)\times 5} and \frac{-93y}{\left(1+12y\right)\times 5} have the same denominator, add them by adding their numerators.

$$\frac{-31-93y}{\left(1+12y\right)\times 5}$$

Expand \left(1+12y\right)\times 5.

$$\frac{-31-93y}{60y+5}$$

Expand

$$-\frac{31\left(3y+1\right)}{5\left(12y+1\right)}$$

Short Solution Steps

Add 1 and 61 to get 62.

$$\left(-\frac{1}{1+12y}\right)\times \frac{\left(1+3y\right)\times 62}{10}$$

Divide \left(1+3y\right)\times 62 by 10 to get \left(1+3y\right)\times \frac{31}{5}.

$$\left(-\frac{1}{1+12y}\right)\left(1+3y\right)\times \frac{31}{5}$$

Use the distributive property to multiply 1+3y by \frac{31}{5}.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+3y\times \frac{31}{5}\right)$$

Express 3\times \frac{31}{5} as a single fraction.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+\frac{3\times 31}{5}y\right)$$

Multiply 3 and 31 to get 93.

$$\left(-\frac{1}{1+12y}\right)\left(\frac{31}{5}+\frac{93}{5}y\right)$$

Use the distributive property to multiply -\frac{1}{1+12y} by \frac{31}{5}+\frac{93}{5}y.

$$\left(-\frac{1}{1+12y}\right)\times \frac{31}{5}+\left(-\frac{1}{1+12y}\right)\times \frac{93}{5}y$$

Multiply -\frac{1}{1+12y} times \frac{31}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31}{\left(1+12y\right)\times 5}+\left(-\frac{1}{1+12y}\right)\times \frac{93}{5}y$$

Multiply -\frac{1}{1+12y} times \frac{93}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31}{\left(1+12y\right)\times 5}+\frac{-93}{\left(1+12y\right)\times 5}y$$

Express \frac{-93}{\left(1+12y\right)\times 5}y as a single fraction.

$$\frac{-31}{\left(1+12y\right)\times 5}+\frac{-93y}{\left(1+12y\right)\times 5}$$

Since \frac{-31}{\left(1+12y\right)\times 5} and \frac{-93y}{\left(1+12y\right)\times 5} have the same denominator, add them by adding their numerators.

$$\frac{-31-93y}{\left(1+12y\right)\times 5}$$

Expand \left(1+12y\right)\times 5.

$$\frac{-31-93y}{60y+5}$$