Example

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

Question

$$( \operatorname { S i m p l i f y } ) : \frac { 1 } { x + 1 } + \frac { 2 } { 1 + x ^ { 2 } } - \frac { 4 } { 1 - x ^ { 4 } } \quad [ 3 ]$$

Answer

$$(Si*3]1*IM*m*p*l*f*y*(1+x^2)*(1-x)+2*(1+x)*(1-x)-4*An*s)/((1+x)*(1+x^2)*(1-x))$$

Solution


Remove parentheses.
Regroup terms.
Rewrite \(1-{x}^{4}\) in the form \({a}^{2}-{b}^{2}\), where \(a=1\) and \(b={x}^{2}\).
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
Rewrite \(1-{x}^{2}\) in the form \({a}^{2}-{b}^{2}\), where \(a=1\) and \(b=x\).
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
Simplify.
Rewrite the expression with a common denominator.
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