Solve 3(4y^2+10y-7)/16y^2-9=3y-7/3-4y+6y+5/3+4y

$$\frac { 3 ( 4 y ^ { 2 } + 10 y - 7 ) } { 16 y ^ { 2 } - 9 } = \frac { 3 y - 7 } { 3 - 4 y } + \frac { 6 y + 5 } { 3 + 4 y }$$

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -\frac{3}{4},\frac{3}{4} since division by zero is not defined. Multiply both sides of the equation by \left(4y-3\right)\left(4y+3\right), the least common multiple of 16y^{2}-9,3-4y,3+4y.

$$3\left(4y^{2}+10y-7\right)=\left(-3-4y\right)\left(3y-7\right)+\left(4y-3\right)\left(6y+5\right)$$

Use the distributive property to multiply 3 by 4y^{2}+10y-7.

$$12y^{2}+30y-21=\left(-3-4y\right)\left(3y-7\right)+\left(4y-3\right)\left(6y+5\right)$$

Use the distributive property to multiply -3-4y by 3y-7 and combine like terms.

$$12y^{2}+30y-21=19y+21-12y^{2}+\left(4y-3\right)\left(6y+5\right)$$

Use the distributive property to multiply 4y-3 by 6y+5 and combine like terms.

$$12y^{2}+30y-21=19y+21-12y^{2}+24y^{2}+2y-15$$

Combine -12y^{2} and 24y^{2} to get 12y^{2}.

$$12y^{2}+30y-21=19y+21+12y^{2}+2y-15$$

Combine 19y and 2y to get 21y.

$$12y^{2}+30y-21=21y+21+12y^{2}-15$$

Subtract 15 from 21 to get 6.

$$12y^{2}+30y-21=21y+6+12y^{2}$$

Subtract 21y from both sides.

$$12y^{2}+30y-21-21y=6+12y^{2}$$

Combine 30y and -21y to get 9y.

$$12y^{2}+9y-21=6+12y^{2}$$

Subtract 12y^{2} from both sides.

$$12y^{2}+9y-21-12y^{2}=6$$

Combine 12y^{2} and -12y^{2} to get 0.

$$9y-21=6$$

Add 21 to both sides.

$$9y=6+21$$

Add 6 and 21 to get 27.

$$9y=27$$

Divide both sides by 9.

$$y=\frac{27}{9}$$

Divide 27 by 9 to get 3.

$$y=3$$