Solve - [x] = 3/(2 ^ 2 * (s + 1)(s + 4)) - 1/(s(s + 1)) | 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

$$-[x]=\frac{3}{2^{2}(s+1)(s+4)}-\frac{1}{s(s+1)}$$

Solve for x

$x=\frac{s+16}{4s\left(s+1\right)\left(s+4\right)}$
$s\neq -4\text{ and }s\neq -1\text{ and }s\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $4s\left(s+1\right)\left(s+4\right)$, the least common multiple of $2^{2}\left(s+1\right)\left(s+4\right),s\left(s+1\right)$.

$$-4s\left(s+1\right)\left(s+4\right)x=s\times 3-\left(4s+16\right)$$

Use the distributive property to multiply $4s$ by $s+1$.

$$-\left(4s^{2}+4s\right)\left(s+4\right)x=s\times 3-\left(4s+16\right)$$

Use the distributive property to multiply $4s^{2}+4s$ by $s+4$ and combine like terms.

$$-\left(4s^{3}+20s^{2}+16s\right)x=s\times 3-\left(4s+16\right)$$

Use the distributive property to multiply $4s^{3}+20s^{2}+16s$ by $x$.

$$-\left(4s^{3}x+20s^{2}x+16sx\right)=s\times 3-\left(4s+16\right)$$

To find the opposite of $4s^{3}x+20s^{2}x+16sx$, find the opposite of each term.

$$-4s^{3}x-20s^{2}x-16sx=s\times 3-\left(4s+16\right)$$

To find the opposite of $4s+16$, find the opposite of each term.

$$-4s^{3}x-20s^{2}x-16sx=s\times 3-4s-16$$

Combine $s\times 3$ and $-4s$ to get $-s$.

$$-4s^{3}x-20s^{2}x-16sx=-s-16$$

Combine all terms containing $x$.

$$\left(-4s^{3}-20s^{2}-16s\right)x=-s-16$$

Divide both sides by $-4s^{3}-20s^{2}-16s$.

$$\frac{\left(-4s^{3}-20s^{2}-16s\right)x}{-4s^{3}-20s^{2}-16s}=\frac{-s-16}{-4s^{3}-20s^{2}-16s}$$

Dividing by $-4s^{3}-20s^{2}-16s$ undoes the multiplication by $-4s^{3}-20s^{2}-16s$.

$$x=\frac{-s-16}{-4s^{3}-20s^{2}-16s}$$

Divide $-s-16$ by $-4s^{3}-20s^{2}-16s$.

$$x=\frac{s+16}{4s\left(s+1\right)\left(s+4\right)}$$