Example

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

Question

$$x ^ { 2 } x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 18 x ^ { 3 } - \frac { 1 } { x ^ { 3 } }$$

Answer

$$f=-(IM*(18*x^3-1/x^3-1/x^2))/x^2$$

Solution


Regroup terms.
\[\frac{1}{{x}^{2}}+\imath f{x}^{2}=18{x}^{3}-\frac{1}{{x}^{3}}\]
Subtract \(\frac{1}{{x}^{2}}\) from both sides.
\[\imath f{x}^{2}=18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}}\]
Divide both sides by \(\imath \).
\[f{x}^{2}=\frac{18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}}}{\imath }\]
Rationalize the denominator: \(\frac{18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}}}{\imath } \cdot \frac{\imath }{\imath }=-(18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}})\imath \).
\[f{x}^{2}=-(18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}})\imath \]
Regroup terms.
\[f{x}^{2}=-\imath (18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}})\]
Divide both sides by \({x}^{2}\).
\[f=-\frac{\imath (18{x}^{3}-\frac{1}{{x}^{3}}-\frac{1}{{x}^{2}})}{{x}^{2}}\]
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