Solve (2)/(x+1)-(6)/(2x-1)+(3)/(3x+2)=0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ 2 }{ x+1 } - \frac{ 6 }{ 2x-1 } + \frac{ 3 }{ 3x+2 } =0$$

Solve for x

$x=-\frac{19}{25}=-0.76$

Steps for Solving Linear Equation

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

$$\left(x+6x^{2}-2\right)\times 2-\left(x+1\right)\left(2+3x\right)\times 6+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Use the distributive property to multiply $x+6x^{2}-2$ by $2$.

$$2x+12x^{2}-4-\left(x+1\right)\left(2+3x\right)\times 6+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Use the distributive property to multiply $x+1$ by $2+3x$ and combine like terms.

$$2x+12x^{2}-4-\left(5x+3x^{2}+2\right)\times 6+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Use the distributive property to multiply $5x+3x^{2}+2$ by $6$.

$$2x+12x^{2}-4-\left(30x+18x^{2}+12\right)+\left(2x-1\right)\left(x+1\right)\times 3=0$$

To find the opposite of $30x+18x^{2}+12$, find the opposite of each term.

$$2x+12x^{2}-4-30x-18x^{2}-12+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Combine $2x$ and $-30x$ to get $-28x$.

$$-28x+12x^{2}-4-18x^{2}-12+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Combine $12x^{2}$ and $-18x^{2}$ to get $-6x^{2}$.

$$-28x-6x^{2}-4-12+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Subtract $12$ from $-4$ to get $-16$.

$$-28x-6x^{2}-16+\left(2x-1\right)\left(x+1\right)\times 3=0$$

Use the distributive property to multiply $2x-1$ by $x+1$ and combine like terms.

$$-28x-6x^{2}-16+\left(2x^{2}+x-1\right)\times 3=0$$

Use the distributive property to multiply $2x^{2}+x-1$ by $3$.

$$-28x-6x^{2}-16+6x^{2}+3x-3=0$$

Combine $-6x^{2}$ and $6x^{2}$ to get $0$.

$$-28x-16+3x-3=0$$

Combine $-28x$ and $3x$ to get $-25x$.

$$-25x-16-3=0$$

Subtract $3$ from $-16$ to get $-19$.

$$-25x-19=0$$

Add $19$ to both sides. Anything plus zero gives itself.

$$-25x=19$$

Divide both sides by $-25$.

$$x=\frac{19}{-25}$$

Fraction $\frac{19}{-25}$ can be rewritten as $-\frac{19}{25}$ by extracting the negative sign.

$$x=-\frac{19}{25}$$