Solve 4/9y^2-1-4/3y+1=5/1-3y

$$\frac { 4 } { 9 y ^ { 2 } - 1 } - \frac { 4 } { 3 y + 1 } = \frac { 5 } { 1 - 3 y }$$

Solve for y

$$y = -\frac{13}{3} = -4\frac{1}{3} \approx -4.333333333$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -\frac{1}{3},\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3y-1\right)\left(3y+1\right), the least common multiple of 9y^{2}-1,3y+1,1-3y.

$$4-\left(3y-1\right)\times 4=\left(-1-3y\right)\times 5$$

Use the distributive property to multiply 3y-1 by 4.

$$4-\left(12y-4\right)=\left(-1-3y\right)\times 5$$

To find the opposite of 12y-4, find the opposite of each term.

$$4-12y+4=\left(-1-3y\right)\times 5$$

Add 4 and 4 to get 8.

$$8-12y=\left(-1-3y\right)\times 5$$

Use the distributive property to multiply -1-3y by 5.

$$8-12y=-5-15y$$

Add 15y to both sides.

$$8-12y+15y=-5$$

Combine -12y and 15y to get 3y.

$$8+3y=-5$$

Subtract 8 from both sides.

$$3y=-5-8$$

Subtract 8 from -5 to get -13.

$$3y=-13$$

Divide both sides by 3.

$$y=\frac{-13}{3}$$

Fraction \frac{-13}{3} can be rewritten as -\frac{13}{3} by extracting the negative sign.

$$y=-\frac{13}{3}$$