Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\left. \begin{array} { l } { : \frac { x ^ { 3 } - 4 - x + 4 x ^ { 2 } } { x ^ { 2 } + 3 x - 4 } } \end{array} \right.$$

Answer

Si*Ba*e*IM*m*p*l*f*y*s*d*(x+1)

Solution


Factor \({x}^{3}-4-x+4{x}^{2}\) using Polynomial Division.
\[x^2\]\[5x\]\[4\]
\[x-1\]\[x^3\]\[4x^2\]\[-x\]\[-4\]
\[x^3\]\[-x^2\]
\[5x^2\]\[-x\]\[-4\]
\[5x^2\]\[-5x\]
\[4x\]\[-4\]
\[4x\]\[-4\]
\[\]
Rewrite the expression using the above.
\[{x}^{2}+5x+4\]
\[Simpl\imath fy\times \frac{({x}^{2}+5x+4)(x-1)}{{x}^{2}+3x-4}Based\]
Factor \({x}^{2}+5x+4\).
\[Simpl\imath fy\times \frac{(x+1)(x+4)(x-1)}{{x}^{2}+3x-4}Based\]
Factor \({x}^{2}+3x-4\).
\[Simpl\imath fy\times \frac{(x+1)(x+4)(x-1)}{(x-1)(x+4)}Based\]
Cancel \(x-1\).
\[Simpl\imath fy\times \frac{(x+1)(x+4)}{x+4}Based\]
Cancel \(x+4\).
\[Simpl\imath fy(x+1)Based\]
Regroup terms.
\[SiBae\imath mplfysd(x+1)\]
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