Solve for a (complex solution)
\left\{\begin{matrix}a=x^{2}-4\text{, }&x\neq 2\text{ and }x\neq -2\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=x^{2}-4\text{, }&|x|\neq 2\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\sqrt{a+4}\text{; }x=\sqrt{a+4}\text{, }&a\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt{a+4}\text{; }x=-\sqrt{a+4}\text{, }&a\neq 0\text{ and }a\geq -4\end{matrix}\right.
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a\left(\frac{x+1}{x-2}-\frac{x-1}{x+2}\right)\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x-2,x+2.
a\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\right)\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+1}{x-2} times \frac{x+2}{x+2}. Multiply \frac{x-1}{x+2} times \frac{x-2}{x-2}.
a\times \frac{\left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Since \frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
a\times \frac{x^{2}+2x+x+2-x^{2}+2x+x-2}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Do the multiplications in \left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x-2\right).
a\times \frac{6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Combine like terms in x^{2}+2x+x+2-x^{2}+2x+x-2.
\frac{a\times 6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Express a\times \frac{6x}{\left(x-2\right)\left(x+2\right)} as a single fraction.
\frac{a\times 6x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Express \frac{a\times 6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right) as a single fraction.
\frac{6ax}{x+2}\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Cancel out x-2 in both numerator and denominator.
\frac{6ax\left(x+2\right)}{x+2}=6x\left(x-2\right)\left(x+2\right)
Express \frac{6ax}{x+2}\left(x+2\right) as a single fraction.
6ax=6x\left(x-2\right)\left(x+2\right)
Cancel out x+2 in both numerator and denominator.
6ax=\left(6x^{2}-12x\right)\left(x+2\right)
Use the distributive property to multiply 6x by x-2.
6ax=6x^{3}-24x
Use the distributive property to multiply 6x^{2}-12x by x+2 and combine like terms.
6xa=6x^{3}-24x
The equation is in standard form.
\frac{6xa}{6x}=\frac{6x^{3}-24x}{6x}
Divide both sides by 6x.
a=\frac{6x^{3}-24x}{6x}
Dividing by 6x undoes the multiplication by 6x.
a=x^{2}-4
Divide 6x^{3}-24x by 6x.
a\left(\frac{x+1}{x-2}-\frac{x-1}{x+2}\right)\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Multiply both sides of the equation by \left(x-2\right)\left(x+2\right), the least common multiple of x-2,x+2.
a\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\right)\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{x+1}{x-2} times \frac{x+2}{x+2}. Multiply \frac{x-1}{x+2} times \frac{x-2}{x-2}.
a\times \frac{\left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Since \frac{\left(x+1\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
a\times \frac{x^{2}+2x+x+2-x^{2}+2x+x-2}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Do the multiplications in \left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x-2\right).
a\times \frac{6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Combine like terms in x^{2}+2x+x+2-x^{2}+2x+x-2.
\frac{a\times 6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right)\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Express a\times \frac{6x}{\left(x-2\right)\left(x+2\right)} as a single fraction.
\frac{a\times 6x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Express \frac{a\times 6x}{\left(x-2\right)\left(x+2\right)}\left(x-2\right) as a single fraction.
\frac{6ax}{x+2}\left(x+2\right)=6x\left(x-2\right)\left(x+2\right)
Cancel out x-2 in both numerator and denominator.
\frac{6ax\left(x+2\right)}{x+2}=6x\left(x-2\right)\left(x+2\right)
Express \frac{6ax}{x+2}\left(x+2\right) as a single fraction.
6ax=6x\left(x-2\right)\left(x+2\right)
Cancel out x+2 in both numerator and denominator.
6ax=\left(6x^{2}-12x\right)\left(x+2\right)
Use the distributive property to multiply 6x by x-2.
6ax=6x^{3}-24x
Use the distributive property to multiply 6x^{2}-12x by x+2 and combine like terms.
6xa=6x^{3}-24x
The equation is in standard form.
\frac{6xa}{6x}=\frac{6x^{3}-24x}{6x}
Divide both sides by 6x.
a=\frac{6x^{3}-24x}{6x}
Dividing by 6x undoes the multiplication by 6x.
a=x^{2}-4
Divide 6x^{3}-24x by 6x.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}