Solve 6x+5/15-5x+2/3x+4=2x+3/5-1

$$\frac { 6 x + 5 } { 15 } - \frac { 5 x + 2 } { 3 x + 4 } = \frac { 2 x + 3 } { 5 } - 1$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 15\left(3x+4\right), the least common multiple of 15,3x+4,5.

$$\left(3x+4\right)\left(6x+5\right)-15\left(5x+2\right)=\left(9x+12\right)\left(2x+3\right)+15\left(3x+4\right)\left(-1\right)$$

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

$$18x^{2}+39x+20-15\left(5x+2\right)=\left(9x+12\right)\left(2x+3\right)+15\left(3x+4\right)\left(-1\right)$$

Use the distributive property to multiply -15 by 5x+2.

$$18x^{2}+39x+20-75x-30=\left(9x+12\right)\left(2x+3\right)+15\left(3x+4\right)\left(-1\right)$$

Combine 39x and -75x to get -36x.

$$18x^{2}-36x+20-30=\left(9x+12\right)\left(2x+3\right)+15\left(3x+4\right)\left(-1\right)$$

Subtract 30 from 20 to get -10.

$$18x^{2}-36x-10=\left(9x+12\right)\left(2x+3\right)+15\left(3x+4\right)\left(-1\right)$$

Use the distributive property to multiply 9x+12 by 2x+3 and combine like terms.

$$18x^{2}-36x-10=18x^{2}+51x+36+15\left(3x+4\right)\left(-1\right)$$

Multiply 15 and -1 to get -15.

$$18x^{2}-36x-10=18x^{2}+51x+36-15\left(3x+4\right)$$

Use the distributive property to multiply -15 by 3x+4.

$$18x^{2}-36x-10=18x^{2}+51x+36-45x-60$$

Combine 51x and -45x to get 6x.

$$18x^{2}-36x-10=18x^{2}+6x+36-60$$

Subtract 60 from 36 to get -24.

$$18x^{2}-36x-10=18x^{2}+6x-24$$

Subtract 18x^{2} from both sides.

$$18x^{2}-36x-10-18x^{2}=6x-24$$

Combine 18x^{2} and -18x^{2} to get 0.

$$-36x-10=6x-24$$

Subtract 6x from both sides.

$$-36x-10-6x=-24$$

Combine -36x and -6x to get -42x.

$$-42x-10=-24$$

Add 10 to both sides.

$$-42x=-24+10$$

Add -24 and 10 to get -14.

$$-42x=-14$$

Divide both sides by -42.

$$x=\frac{-14}{-42}$$

Reduce the fraction \frac{-14}{-42} to lowest terms by extracting and canceling out -14.

$$x=\frac{1}{3}$$