Solve by-5/y+2=-4/3

$$\frac { b y - 5 } { y + 2 } = \frac { - 4 } { 3 }$$

Solve for b

$$b=-\frac{4}{3}+\frac{7}{3y}$$

$$y\neq 0\text{ and }y\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(y+2\right), the least common multiple of y+2,3.

$$3\left(by-5\right)=\left(y+2\right)\left(-4\right)$$

Use the distributive property to multiply 3 by by-5.

$$3by-15=\left(y+2\right)\left(-4\right)$$

Use the distributive property to multiply y+2 by -4.

$$3by-15=-4y-8$$

Add 15 to both sides.

$$3by=-4y-8+15$$

Add -8 and 15 to get 7.

$$3by=-4y+7$$

The equation is in standard form.

$$3yb=7-4y$$

Divide both sides by 3y.

$$\frac{3yb}{3y}=\frac{7-4y}{3y}$$

Dividing by 3y undoes the multiplication by 3y.

$$b=\frac{7-4y}{3y}$$

Divide -4y+7 by 3y.

$$b=-\frac{4}{3}+\frac{7}{3y}$$

Solve for y

$$y=\frac{7}{3b+4}$$

$$b\neq -\frac{5}{2}\text{ and }b\neq -\frac{4}{3}$$

Steps for Solving Linear Equation

Variable y cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 3\left(y+2\right), the least common multiple of y+2,3.

$$3\left(by-5\right)=\left(y+2\right)\left(-4\right)$$

Use the distributive property to multiply 3 by by-5.

$$3by-15=\left(y+2\right)\left(-4\right)$$

Use the distributive property to multiply y+2 by -4.

$$3by-15=-4y-8$$

Add 4y to both sides.

$$3by-15+4y=-8$$

Add 15 to both sides.

$$3by+4y=-8+15$$

Add -8 and 15 to get 7.

$$3by+4y=7$$

Combine all terms containing y.

$$\left(3b+4\right)y=7$$

Divide both sides by 4+3b.

$$\frac{\left(3b+4\right)y}{3b+4}=\frac{7}{3b+4}$$

Dividing by 4+3b undoes the multiplication by 4+3b.

$$y=\frac{7}{3b+4}$$

Variable y cannot be equal to -2.

$$y=\frac{7}{3b+4}\text{, }y\neq -2$$