Solve (2)/(2x-3)+(5)/((2x-3)^(2))=(3)/(3x-2) | 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

$$\frac{ 2 }{ 2x-3 } + \frac{ 5 }{ { \left(2x-3 \right) }^{ 2 } } = \frac{ 3 }{ 3x-2 }$$

Solve for x

$x=1$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to any of the values $\frac{2}{3},\frac{3}{2}$ since division by zero is not defined. Multiply both sides of the equation by $6\left(\frac{1}{2}x-\frac{1}{3}\right)\left(2x-3\right)^{2}$, the least common multiple of $2x-3,\left(2x-3\right)^{2},3x-2$.

$$\left(-2+3x\right)\left(2x-3\right)\times 2+\left(-2+3x\right)\times 5=\left(2x-3\right)^{2}\times 3$$

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

$$\left(-13x+6+6x^{2}\right)\times 2+\left(-2+3x\right)\times 5=\left(2x-3\right)^{2}\times 3$$

Use the distributive property to multiply $-13x+6+6x^{2}$ by $2$.

$$-26x+12+12x^{2}+\left(-2+3x\right)\times 5=\left(2x-3\right)^{2}\times 3$$

Use the distributive property to multiply $-2+3x$ by $5$.

$$-26x+12+12x^{2}-10+15x=\left(2x-3\right)^{2}\times 3$$

Subtract $10$ from $12$ to get $2$.

$$-26x+2+12x^{2}+15x=\left(2x-3\right)^{2}\times 3$$

Combine $-26x$ and $15x$ to get $-11x$.

$$-11x+2+12x^{2}=\left(2x-3\right)^{2}\times 3$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-3\right)^{2}$.

$$-11x+2+12x^{2}=\left(4x^{2}-12x+9\right)\times 3$$

Use the distributive property to multiply $4x^{2}-12x+9$ by $3$.

$$-11x+2+12x^{2}=12x^{2}-36x+27$$

Subtract $12x^{2}$ from both sides.

$$-11x+2+12x^{2}-12x^{2}=-36x+27$$

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

$$-11x+2=-36x+27$$

Add $36x$ to both sides.

$$-11x+2+36x=27$$

Combine $-11x$ and $36x$ to get $25x$.

$$25x+2=27$$

Subtract $2$ from both sides.

$$25x=27-2$$

Subtract $2$ from $27$ to get $25$.

$$25x=25$$

Divide both sides by $25$.

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

Divide $25$ by $25$ to get $1$.

$$x=1$$