Solve for y (complex solution)
y=-\frac{x}{-2x^{4}+5x+4\sqrt{x}+3}
x\neq 0\text{ and }-2x^{4}+5x+4\sqrt{x}\neq -3\text{ and }-2x^{4}+5x+4\sqrt{x}+3\neq 0
Solve for y
y=-\frac{x}{-2x^{4}+5x+4\sqrt{x}+3}
-2x^{4}+5x+4\sqrt{x}\neq -3\text{ and }x>0
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x=2x^{3}xy-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of y,x.
x=2x^{4}y-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
2x^{4}y-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)=x
Swap sides so that all variable terms are on the left hand side.
2yx^{4}-5xy-4\sqrt{x}y-3y=x
Reorder the terms.
\left(2x^{4}-5x-4\sqrt{x}-3\right)y=x
Combine all terms containing y.
\frac{\left(2x^{4}-5x-4\sqrt{x}-3\right)y}{2x^{4}-5x-4\sqrt{x}-3}=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}
Divide both sides by 2x^{4}-5x-4\sqrt{x}-3.
y=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}
Dividing by 2x^{4}-5x-4\sqrt{x}-3 undoes the multiplication by 2x^{4}-5x-4\sqrt{x}-3.
y=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}\text{, }y\neq 0
Variable y cannot be equal to 0.
x=2x^{3}xy-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of y,x.
x=2x^{4}y-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
2x^{4}y-y\times 3-yx^{\frac{1}{2}}\times 4+xy\left(-5\right)=x
Swap sides so that all variable terms are on the left hand side.
2yx^{4}-5xy-4\sqrt{x}y-3y=x
Reorder the terms.
\left(2x^{4}-5x-4\sqrt{x}-3\right)y=x
Combine all terms containing y.
\frac{\left(2x^{4}-5x-4\sqrt{x}-3\right)y}{2x^{4}-5x-4\sqrt{x}-3}=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}
Divide both sides by 2x^{4}-5x-4\sqrt{x}-3.
y=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}
Dividing by 2x^{4}-5x-4\sqrt{x}-3 undoes the multiplication by 2x^{4}-5x-4\sqrt{x}-3.
y=\frac{x}{2x^{4}-5x-4\sqrt{x}-3}\text{, }y\neq 0
Variable y cannot be equal to 0.
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