Solve 1+4b/b=1-4y/y

$$\frac { 1 + 4 b } { b } = \frac { 1 - 4 y } { y }$$

Solve for b

$$b=-\frac{y}{8y-1}$$

$$y\neq 0\text{ and }y\neq \frac{1}{8}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by by, the least common multiple of b,y.

$$y\left(1+4b\right)=b\left(1-4y\right)$$

Use the distributive property to multiply y by 1+4b.

$$y+4yb=b\left(1-4y\right)$$

Use the distributive property to multiply b by 1-4y.

$$y+4yb=b-4by$$

Subtract b from both sides.

$$y+4yb-b=-4by$$

Add 4by to both sides.

$$y+4yb-b+4by=0$$

Combine 4yb and 4by to get 8yb.

$$y+8yb-b=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$8yb-b=-y$$

Combine all terms containing b.

$$\left(8y-1\right)b=-y$$

Divide both sides by 8y-1.

$$\frac{\left(8y-1\right)b}{8y-1}=-\frac{y}{8y-1}$$

Dividing by 8y-1 undoes the multiplication by 8y-1.

$$b=-\frac{y}{8y-1}$$

Variable b cannot be equal to 0.

$$b=-\frac{y}{8y-1}\text{, }b\neq 0$$

Solve for y

$$y=\frac{b}{8b+1}$$

$$b\neq 0\text{ and }b\neq -\frac{1}{8}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by by, the least common multiple of b,y.

$$y\left(1+4b\right)=b\left(1-4y\right)$$

Use the distributive property to multiply y by 1+4b.

$$y+4yb=b\left(1-4y\right)$$

Use the distributive property to multiply b by 1-4y.

$$y+4yb=b-4by$$

Add 4by to both sides.

$$y+4yb+4by=b$$

Combine 4yb and 4by to get 8yb.

$$y+8yb=b$$

Combine all terms containing y.

$$\left(1+8b\right)y=b$$

The equation is in standard form.

$$\left(8b+1\right)y=b$$

Divide both sides by 1+8b.

$$\frac{\left(8b+1\right)y}{8b+1}=\frac{b}{8b+1}$$

Dividing by 1+8b undoes the multiplication by 1+8b.

$$y=\frac{b}{8b+1}$$

Variable y cannot be equal to 0.

$$y=\frac{b}{8b+1}\text{, }y\neq 0$$