Solve for x
x=-\frac{3}{5}=-0.6
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x+3-\left(x+\frac{9}{2}+\frac{9}{2x}\right)=6
Multiply both sides of the equation by 2.
x+3-\left(x+\frac{9x}{2x}+\frac{9}{2x}\right)=6
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2x is 2x. Multiply \frac{9}{2} times \frac{x}{x}.
x+3-\left(x+\frac{9x+9}{2x}\right)=6
Since \frac{9x}{2x} and \frac{9}{2x} have the same denominator, add them by adding their numerators.
x+3-x-\frac{9x+9}{2x}=6
To find the opposite of x+\frac{9x+9}{2x}, find the opposite of each term.
x+3-\frac{x\times 2x}{2x}-\frac{9x+9}{2x}=6
To add or subtract expressions, expand them to make their denominators the same. Multiply -x times \frac{2x}{2x}.
x+3+\frac{-x\times 2x-\left(9x+9\right)}{2x}=6
Since -\frac{x\times 2x}{2x} and \frac{9x+9}{2x} have the same denominator, subtract them by subtracting their numerators.
x+3+\frac{-2x^{2}-9x-9}{2x}=6
Do the multiplications in -x\times 2x-\left(9x+9\right).
\frac{\left(x+3\right)\times 2x}{2x}+\frac{-2x^{2}-9x-9}{2x}=6
To add or subtract expressions, expand them to make their denominators the same. Multiply x+3 times \frac{2x}{2x}.
\frac{\left(x+3\right)\times 2x-2x^{2}-9x-9}{2x}=6
Since \frac{\left(x+3\right)\times 2x}{2x} and \frac{-2x^{2}-9x-9}{2x} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+6x-2x^{2}-9x-9}{2x}=6
Do the multiplications in \left(x+3\right)\times 2x-2x^{2}-9x-9.
\frac{-3x-9}{2x}=6
Combine like terms in 2x^{2}+6x-2x^{2}-9x-9.
-3x-9=12x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x.
-3x-9-12x=0
Subtract 12x from both sides.
-15x-9=0
Combine -3x and -12x to get -15x.
-15x=9
Add 9 to both sides. Anything plus zero gives itself.
x=\frac{9}{-15}
Divide both sides by -15.
x=-\frac{3}{5}
Reduce the fraction \frac{9}{-15} to lowest terms by extracting and canceling out 3.
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}