Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{Findthevaluesofandyx}{2+\imath }-\frac{1-5\imath }{3-2\imath }+\frac{y}{2-\imath }\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{Fi{n}^{2}{d}^{2}th{e}^{2}v{a}^{2}lusofyx}{2+\imath }-\frac{1-5\imath }{3-2\imath }+\frac{y}{2-\imath }\]
Regroup terms.
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{1-5\imath }{3-2\imath }+\frac{y}{2-\imath }\]
Rationalize the denominator: \(\frac{1-5\imath }{3-2\imath } \cdot \frac{3+2\imath }{3+2\imath }=\frac{3+2\imath -15\imath +10}{{3}^{2}-{(2\imath )}^{2}}\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{3+2\imath -15\imath +10}{{3}^{2}-{(2\imath )}^{2}}+\frac{y}{2-\imath }\]
Collect like terms.
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{(3+10)+(2\imath -15\imath )}{{3}^{2}-{(2\imath )}^{2}}+\frac{y}{2-\imath }\]
Simplify \((3+10)+(2\imath -15\imath )\) to \(13-13\imath \).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{{3}^{2}-{(2\imath )}^{2}}+\frac{y}{2-\imath }\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9-{(2\imath )}^{2}}+\frac{y}{2-\imath }\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9-{2}^{2}{\imath }^{2}}+\frac{y}{2-\imath }\]
Simplify \({2}^{2}\) to \(4\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9-4{\imath }^{2}}+\frac{y}{2-\imath }\]
Use Square Rule: \({i}^{2}=-1\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9-4\times -1}+\frac{y}{2-\imath }\]
Simplify \(4\times -1\) to \(-4\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9-(-4)}+\frac{y}{2-\imath }\]
Remove parentheses.
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{9+4}+\frac{y}{2-\imath }\]
Simplify \(9+4\) to \(13\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13-13\imath }{13}+\frac{y}{2-\imath }\]
Factor out the common term \(13\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-\frac{13(1-\imath )}{13}+\frac{y}{2-\imath }\]
Cancel \(13\).
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-(1-\imath )+\frac{y}{2-\imath }\]
Remove parentheses.
\[\frac{Fi{e}^{2}{n}^{2}{d}^{2}thv{a}^{2}lusofyx}{2+\imath }-1+\imath +\frac{y}{2-\imath }\]
(Fi*e^2*n^2*d^2*t*h*v*a^2*l*u*s*o*f*y*x)/(2+IM)-1+IM+y/(2-IM)
