Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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2x+\sqrt{3}x=\frac{x}{2-\sqrt{3}}
Use the distributive property to multiply 2+\sqrt{3} by x.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}
Rationalize the denominator of \frac{x}{2-\sqrt{3}} by multiplying numerator and denominator by 2+\sqrt{3}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{4-3}
Square 2. Square \sqrt{3}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{1}
Subtract 3 from 4 to get 1.
2x+\sqrt{3}x=x\left(2+\sqrt{3}\right)
Anything divided by one gives itself.
2x+\sqrt{3}x=2x+x\sqrt{3}
Use the distributive property to multiply x by 2+\sqrt{3}.
2x+\sqrt{3}x-2x=x\sqrt{3}
Subtract 2x from both sides.
\sqrt{3}x=x\sqrt{3}
Combine 2x and -2x to get 0.
\sqrt{3}x-x\sqrt{3}=0
Subtract x\sqrt{3} from both sides.
0=0
Combine \sqrt{3}x and -x\sqrt{3} to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
2x+\sqrt{3}x=\frac{x}{2-\sqrt{3}}
Use the distributive property to multiply 2+\sqrt{3} by x.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}
Rationalize the denominator of \frac{x}{2-\sqrt{3}} by multiplying numerator and denominator by 2+\sqrt{3}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{2^{2}-\left(\sqrt{3}\right)^{2}}
Consider \left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{4-3}
Square 2. Square \sqrt{3}.
2x+\sqrt{3}x=\frac{x\left(2+\sqrt{3}\right)}{1}
Subtract 3 from 4 to get 1.
2x+\sqrt{3}x=x\left(2+\sqrt{3}\right)
Anything divided by one gives itself.
2x+\sqrt{3}x=2x+x\sqrt{3}
Use the distributive property to multiply x by 2+\sqrt{3}.
2x+\sqrt{3}x-2x=x\sqrt{3}
Subtract 2x from both sides.
\sqrt{3}x=x\sqrt{3}
Combine 2x and -2x to get 0.
\sqrt{3}x-x\sqrt{3}=0
Subtract x\sqrt{3} from both sides.
0=0
Combine \sqrt{3}x and -x\sqrt{3} to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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