Solve f(x)=(1+(x)^(3)+(x)^(6))/((x)^(3))(SHOWED)f((x)^(2))=f((x)^(-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

$$f(x)= \frac{ 1+ { x }^{ 3 } + { x }^{ 6 } }{ { x }^{ 3 } } (SHOWED)f( { x }^{ 2 } )=f( { x }^{ -2 } )$$

Solve for D

$\left\{\begin{matrix}D=\frac{1}{EHOSWx\left(x^{6}+x^{3}+1\right)}\text{, }&E\neq 0\text{ and }W\neq 0\text{ and }O\neq 0\text{ and }H\neq 0\text{ and }S\neq 0\text{ and }x\neq 0\\D\in \mathrm{R}\text{, }&f=0\text{ and }x\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $x^{3}$.

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

To multiply powers of the same base, add their exponents. Add $-2$ and $3$ to get $1$.

$$\left(1+x^{3}+x^{6}\right)SHOWEDfx^{2}=fx^{1}$$

Use the distributive property to multiply $1+x^{3}+x^{6}$ by $S$.

$$\left(S+x^{3}S+x^{6}S\right)HOWEDfx^{2}=fx^{1}$$

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

$$\left(SH+x^{3}SH+x^{6}SH\right)OWEDfx^{2}=fx^{1}$$

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

$$\left(SHO+x^{3}SHO+x^{6}SHO\right)WEDfx^{2}=fx^{1}$$

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

$$\left(SHOW+x^{3}SHOW+x^{6}SHOW\right)EDfx^{2}=fx^{1}$$

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

$$\left(SHOWE+x^{3}SHOWE+x^{6}SHOWE\right)Dfx^{2}=fx^{1}$$

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

$$\left(SHOWED+x^{3}SHOWED+x^{6}SHOWED\right)fx^{2}=fx^{1}$$

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

$$\left(SHOWEDf+x^{3}SHOWEDf+x^{6}SHOWEDf\right)x^{2}=fx^{1}$$

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

$$SHOWEDfx^{2}+SHOWEDfx^{5}+SHOWEDfx^{8}=fx^{1}$$

Calculate $x$ to the power of $1$ and get $x$.

$$SHOWEDfx^{2}+SHOWEDfx^{5}+SHOWEDfx^{8}=fx$$

Combine all terms containing $D$.

$$\left(SHOWEfx^{2}+SHOWEfx^{5}+SHOWEfx^{8}\right)D=fx$$

The equation is in standard form.

$$\left(EHOSWfx^{8}+EHOSWfx^{5}+EHOSWfx^{2}\right)D=fx$$

Divide both sides by $SHOWEfx^{2}+SHOWEfx^{5}+SHOWEfx^{8}$.

$$\frac{\left(EHOSWfx^{8}+EHOSWfx^{5}+EHOSWfx^{2}\right)D}{EHOSWfx^{8}+EHOSWfx^{5}+EHOSWfx^{2}}=\frac{fx}{EHOSWfx^{8}+EHOSWfx^{5}+EHOSWfx^{2}}$$

Dividing by $SHOWEfx^{2}+SHOWEfx^{5}+SHOWEfx^{8}$ undoes the multiplication by $SHOWEfx^{2}+SHOWEfx^{5}+SHOWEfx^{8}$.

$$D=\frac{fx}{EHOSWfx^{8}+EHOSWfx^{5}+EHOSWfx^{2}}$$

Divide $fx$ by $SHOWEfx^{2}+SHOWEfx^{5}+SHOWEfx^{8}$.

$$D=\frac{1}{EHOSWx\left(x^{6}+x^{3}+1\right)}$$

Solve for E

$\left\{\begin{matrix}E=\frac{1}{DHOSWx\left(x^{6}+x^{3}+1\right)}\text{, }&D\neq 0\text{ and }W\neq 0\text{ and }O\neq 0\text{ and }H\neq 0\text{ and }S\neq 0\text{ and }x\neq 0\\E\in \mathrm{R}\text{, }&f=0\text{ and }x\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $x^{3}$.

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

To multiply powers of the same base, add their exponents. Add $-2$ and $3$ to get $1$.

$$\left(1+x^{3}+x^{6}\right)SHOWEDfx^{2}=fx^{1}$$

Use the distributive property to multiply $1+x^{3}+x^{6}$ by $S$.

$$\left(S+x^{3}S+x^{6}S\right)HOWEDfx^{2}=fx^{1}$$

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

$$\left(SH+x^{3}SH+x^{6}SH\right)OWEDfx^{2}=fx^{1}$$

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

$$\left(SHO+x^{3}SHO+x^{6}SHO\right)WEDfx^{2}=fx^{1}$$

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

$$\left(SHOW+x^{3}SHOW+x^{6}SHOW\right)EDfx^{2}=fx^{1}$$

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

$$\left(SHOWE+x^{3}SHOWE+x^{6}SHOWE\right)Dfx^{2}=fx^{1}$$

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

$$\left(SHOWED+x^{3}SHOWED+x^{6}SHOWED\right)fx^{2}=fx^{1}$$

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

$$\left(SHOWEDf+x^{3}SHOWEDf+x^{6}SHOWEDf\right)x^{2}=fx^{1}$$

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

$$SHOWEDfx^{2}+SHOWEDfx^{5}+SHOWEDfx^{8}=fx^{1}$$

Calculate $x$ to the power of $1$ and get $x$.

$$SHOWEDfx^{2}+SHOWEDfx^{5}+SHOWEDfx^{8}=fx$$

Combine all terms containing $E$.

$$\left(SHOWDfx^{2}+SHOWDfx^{5}+SHOWDfx^{8}\right)E=fx$$

The equation is in standard form.

$$\left(DHOSWfx^{8}+DHOSWfx^{5}+DHOSWfx^{2}\right)E=fx$$

Divide both sides by $SHOWDfx^{2}+SHOWDfx^{5}+SHOWDfx^{8}$.

$$\frac{\left(DHOSWfx^{8}+DHOSWfx^{5}+DHOSWfx^{2}\right)E}{DHOSWfx^{8}+DHOSWfx^{5}+DHOSWfx^{2}}=\frac{fx}{DHOSWfx^{8}+DHOSWfx^{5}+DHOSWfx^{2}}$$

Dividing by $SHOWDfx^{2}+SHOWDfx^{5}+SHOWDfx^{8}$ undoes the multiplication by $SHOWDfx^{2}+SHOWDfx^{5}+SHOWDfx^{8}$.

$$E=\frac{fx}{DHOSWfx^{8}+DHOSWfx^{5}+DHOSWfx^{2}}$$

Divide $fx$ by $SHOWDfx^{2}+SHOWDfx^{5}+SHOWDfx^{8}$.

$$E=\frac{1}{DHOSWx\left(x^{6}+x^{3}+1\right)}$$