Solve y=[x^2 + x -6]/x-2

Function

Evaluate the derivative

Find the domain

$Find the x -intercept/zero$

y^{'} = \frac{x ^{2} + 6}{x ^{2}}

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Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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Solve the equation

$Solve for x$

$Solve for y$

x = \frac{25 + 2 y + y ^{2} + 1 + y}{2} x = \frac{- 25 + 2 y + y ^{2} + 1 + y}{2}

Evaluate

y = \frac{x ^{2} + x - 6}{x} - 2

Swap the sides of the equation

\frac{x ^{2} + x - 6}{x} - 2 = y

Move the constant to the right-hand side and change its sign

\frac{x ^{2} + x - 6}{x} = y + 2

Multiply both sides of the equation by LCD

\frac{x ^{2} + x - 6}{x} \times x = (y + 2) x

Simplify the equation

x^{2} + x - 6 = (y + 2) x

Move the expression to the left side

x^{2} + x - 6 - (y + 2) x = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{2} + x - 6 + (- y - 2) x = 0

Simplify

More Steps

x^{2} + (- 1 - y) x - 6 = 0

Move the constant to the right side

x^{2} + (- 1 - y) x = 0 - (- 6)

Add the terms

x^{2} + (- 1 - y) x = 6

Add the same value to both sides

x^{2} + (- 1 - y) x + \frac{1 + 2 y + y ^{2}}{4} = 6 + \frac{1 + 2 y + y ^{2}}{4}

Evaluate

x^{2} + (- 1 - y) x + \frac{1 + 2 y + y ^{2}}{4} = \frac{25 + 2 y + y ^{2}}{4}

Evaluate

(x - \frac{1 + y}{2})^{2} = \frac{25 + 2 y + y ^{2}}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x - \frac{1 + y}{2} = \pm \frac{25 + 2 y + y ^{2}}{4}

Simplify the expression

More Steps

x - \frac{1 + y}{2} = \pm \frac{25 + 2 y + y ^{2}}{2}

Separate the equation into 2 possible cases

x - \frac{1 + y}{2} = \frac{25 + 2 y + y ^{2}}{2} x - \frac{1 + y}{2} = - \frac{25 + 2 y + y ^{2}}{2}

Calculate

More Steps

x = \frac{25 + 2 y + y ^{2} + 1 + y}{2} x - \frac{1 + y}{2} = - \frac{25 + 2 y + y ^{2}}{2}

Solution

More Steps

x = \frac{25 + 2 y + y ^{2} + 1 + y}{2} x = \frac{- 25 + 2 y + y ^{2} + 1 + y}{2}

Show Solution

Rewrite the equation

Rewrite in polar form

r = \frac{- cos ( θ ) + 25 cos ^{2} ( θ ) - 12 sin ( 2 θ )}{sin ( 2 θ ) - 2 cos ^{2} ( θ )} r = - \frac{cos ( θ ) + 25 cos ^{2} ( θ ) - 12 sin ( 2 θ )}{sin ( 2 θ ) - 2 cos ^{2} ( θ )}

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Y=[x^2 + x 6]/x 2

Function

Evaluate the derivative

Find the domain

$Find the x -intercept/zero$

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Solve the equation

$Solve for x$

$Solve for y$

Rewrite the equation

Rewrite in polar form

Graph

Y=[x^2 + x 6]/x 2

Function

Evaluate the derivative

Find the domain

Find the x-intercept/zero

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Solve the equation

Solve for x

Solve for y

Rewrite the equation

Rewrite in polar form

Graph

$Find the x -intercept/zero$

$Solve for x$

$Solve for y$