Solve for v (complex solution)
v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}
x\neq -3\text{ and }x\neq -1
Solve for v
v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}
x\geq 0
Graph
Share
Copied to clipboard
\sqrt{2x+3}-\sqrt{x}=\left(x+1\right)\left(x+3\right)v
Multiply both sides of the equation by \left(x+1\right)\left(x+3\right).
\sqrt{2x+3}-\sqrt{x}=\left(x^{2}+4x+3\right)v
Use the distributive property to multiply x+1 by x+3 and combine like terms.
\sqrt{2x+3}-\sqrt{x}=x^{2}v+4xv+3v
Use the distributive property to multiply x^{2}+4x+3 by v.
x^{2}v+4xv+3v=\sqrt{2x+3}-\sqrt{x}
Swap sides so that all variable terms are on the left hand side.
\left(x^{2}+4x+3\right)v=\sqrt{2x+3}-\sqrt{x}
Combine all terms containing v.
\frac{\left(x^{2}+4x+3\right)v}{x^{2}+4x+3}=\frac{\sqrt{2x+3}-\sqrt{x}}{x^{2}+4x+3}
Divide both sides by x^{2}+4x+3.
v=\frac{\sqrt{2x+3}-\sqrt{x}}{x^{2}+4x+3}
Dividing by x^{2}+4x+3 undoes the multiplication by x^{2}+4x+3.
v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}
Divide \sqrt{2x+3}-\sqrt{x} by x^{2}+4x+3.
\sqrt{2x+3}-\sqrt{x}=\left(x+1\right)\left(x+3\right)v
Multiply both sides of the equation by \left(x+1\right)\left(x+3\right).
\sqrt{2x+3}-\sqrt{x}=\left(x^{2}+4x+3\right)v
Use the distributive property to multiply x+1 by x+3 and combine like terms.
\sqrt{2x+3}-\sqrt{x}=x^{2}v+4xv+3v
Use the distributive property to multiply x^{2}+4x+3 by v.
x^{2}v+4xv+3v=\sqrt{2x+3}-\sqrt{x}
Swap sides so that all variable terms are on the left hand side.
\left(x^{2}+4x+3\right)v=\sqrt{2x+3}-\sqrt{x}
Combine all terms containing v.
\frac{\left(x^{2}+4x+3\right)v}{x^{2}+4x+3}=\frac{\sqrt{2x+3}-\sqrt{x}}{x^{2}+4x+3}
Divide both sides by x^{2}+4x+3.
v=\frac{\sqrt{2x+3}-\sqrt{x}}{x^{2}+4x+3}
Dividing by x^{2}+4x+3 undoes the multiplication by x^{2}+4x+3.
v=\frac{\sqrt{2x+3}-\sqrt{x}}{\left(x+1\right)\left(x+3\right)}
Divide \sqrt{2x+3}-\sqrt{x} by x^{2}+4x+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}