Solve X find the value of x 1 1/(a + 2) = (4a + 5)/(2a ^ 2 + 5a + 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

$$\frac { x } { 2 a + 1 } + \frac { 1 } { a + 2 } = \frac { 4 a + 5 } { 2 a ^ { 2 } + 5 a + 2 } , x$$

Solve for a (complex solution)

$a\in \mathrm{C}\setminus -\frac{1}{2},-2$
$x=2$

Steps for Solving Linear Equation

Variable $a$ cannot be equal to any of the values $-2,-\frac{1}{2}$ since division by zero is not defined. Multiply both sides of the equation by $\left(a+2\right)\left(2a+1\right)$, the least common multiple of $2a+1,a+2,2a^{2}+5a+2$.

$$\left(a+2\right)x+2a+1=4a+5$$

Use the distributive property to multiply $a+2$ by $x$.

$$ax+2x+2a+1=4a+5$$

Subtract $4a$ from both sides.

$$ax+2x+2a+1-4a=5$$

Combine $2a$ and $-4a$ to get $-2a$.

$$ax+2x-2a+1=5$$

Subtract $2x$ from both sides.

$$ax-2a+1=5-2x$$

Subtract $1$ from both sides.

$$ax-2a=5-2x-1$$

Subtract $1$ from $5$ to get $4$.

$$ax-2a=4-2x$$

Combine all terms containing $a$.

$$\left(x-2\right)a=4-2x$$

Divide both sides by $-2+x$.

$$\frac{\left(x-2\right)a}{x-2}=\frac{4-2x}{x-2}$$

Dividing by $-2+x$ undoes the multiplication by $-2+x$.

$$a=\frac{4-2x}{x-2}$$

Divide $4-2x$ by $-2+x$.

$$a=-2$$

Variable $a$ cannot be equal to $-2$.

$$a\in \emptyset$$

Solve for a

$a\in \mathrm{R}\setminus -\frac{1}{2},-2$
$x=2$

Steps for Solving Linear Equation

Variable $a$ cannot be equal to any of the values $-2,-\frac{1}{2}$ since division by zero is not defined. Multiply both sides of the equation by $\left(a+2\right)\left(2a+1\right)$, the least common multiple of $2a+1,a+2,2a^{2}+5a+2$.

$$\left(a+2\right)x+2a+1=4a+5$$

Use the distributive property to multiply $a+2$ by $x$.

$$ax+2x+2a+1=4a+5$$

Subtract $4a$ from both sides.

$$ax+2x+2a+1-4a=5$$

Combine $2a$ and $-4a$ to get $-2a$.

$$ax+2x-2a+1=5$$

Subtract $2x$ from both sides.

$$ax-2a+1=5-2x$$

Subtract $1$ from both sides.

$$ax-2a=5-2x-1$$

Subtract $1$ from $5$ to get $4$.

$$ax-2a=4-2x$$

Combine all terms containing $a$.

$$\left(x-2\right)a=4-2x$$

Divide both sides by $-2+x$.

$$\frac{\left(x-2\right)a}{x-2}=\frac{4-2x}{x-2}$$

Dividing by $-2+x$ undoes the multiplication by $-2+x$.

$$a=\frac{4-2x}{x-2}$$

Divide $4-2x$ by $-2+x$.

$$a=-2$$

Variable $a$ cannot be equal to $-2$.

$$a\in \emptyset$$

Solve for x

$x=2$
$a\neq -\frac{1}{2}\text{ and }a\neq -2$

Steps for Solving Linear Equation

Multiply both sides of the equation by $\left(a+2\right)\left(2a+1\right)$, the least common multiple of $2a+1,a+2,2a^{2}+5a+2$.

$$\left(a+2\right)x+2a+1=4a+5$$

Use the distributive property to multiply $a+2$ by $x$.

$$ax+2x+2a+1=4a+5$$

Subtract $2a$ from both sides.

$$ax+2x+1=4a+5-2a$$

Combine $4a$ and $-2a$ to get $2a$.

$$ax+2x+1=2a+5$$

Subtract $1$ from both sides.

$$ax+2x=2a+5-1$$

Subtract $1$ from $5$ to get $4$.

$$ax+2x=2a+4$$

Combine all terms containing $x$.

$$\left(a+2\right)x=2a+4$$

Divide both sides by $a+2$.

$$\frac{\left(a+2\right)x}{a+2}=\frac{2a+4}{a+2}$$

Dividing by $a+2$ undoes the multiplication by $a+2$.

$$x=\frac{2a+4}{a+2}$$

Divide $4+2a$ by $a+2$.

$$x=2$$