Solve for L (complex solution)
\left\{\begin{matrix}L=\frac{y}{x\left(x+7\right)}\text{, }&x\neq -7\text{ and }x\neq 0\\L\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=-7\right)\text{ and }y=0\end{matrix}\right.
Solve for L
\left\{\begin{matrix}L=\frac{y}{x\left(x+7\right)}\text{, }&x\neq -7\text{ and }x\neq 0\\L\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=-7\right)\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{4Ly+49L^{2}}}{2L}-\frac{7}{2}\text{; }x=-\frac{\sqrt{4Ly+49L^{2}}}{2L}-\frac{7}{2}\text{, }&L\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }L=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{4Ly+49L^{2}}}{2L}-\frac{7}{2}\text{; }x=-\frac{\sqrt{4Ly+49L^{2}}}{2L}-\frac{7}{2}\text{, }&\left(y\leq -\frac{49L}{4}\text{ and }L<0\right)\text{ or }\left(y\geq -\frac{49L}{4}\text{ and }L>0\right)\text{ or }\left(L\neq 0\text{ and }y=-\frac{49L}{4}\right)\\x\in \mathrm{R}\text{, }&y=0\text{ and }L=0\end{matrix}\right.
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y=Lx^{2}+7Lx
Use the distributive property to multiply L by x^{2}+7x.
Lx^{2}+7Lx=y
Swap sides so that all variable terms are on the left hand side.
\left(x^{2}+7x\right)L=y
Combine all terms containing L.
\frac{\left(x^{2}+7x\right)L}{x^{2}+7x}=\frac{y}{x^{2}+7x}
Divide both sides by x^{2}+7x.
L=\frac{y}{x^{2}+7x}
Dividing by x^{2}+7x undoes the multiplication by x^{2}+7x.
L=\frac{y}{x\left(x+7\right)}
Divide y by x^{2}+7x.
y=Lx^{2}+7Lx
Use the distributive property to multiply L by x^{2}+7x.
Lx^{2}+7Lx=y
Swap sides so that all variable terms are on the left hand side.
\left(x^{2}+7x\right)L=y
Combine all terms containing L.
\frac{\left(x^{2}+7x\right)L}{x^{2}+7x}=\frac{y}{x^{2}+7x}
Divide both sides by x^{2}+7x.
L=\frac{y}{x^{2}+7x}
Dividing by x^{2}+7x undoes the multiplication by x^{2}+7x.
L=\frac{y}{x\left(x+7\right)}
Divide y by x^{2}+7x.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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