Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x/3)=-1/2
-
Equation (x^2-1)/(x+2)=4x
-
Equation tan(x)=-1
-
Equation (7-10x)-(8-8x)+(10x+6)=-8
- Express {x} in terms of y where:
- -5*x+5*y=-9
- 1*x+7*y=8
- 4*x-13*y=13
- 4*x+3*y=-15
- Graphing y =:
- (x^2-1)/(x+2)
- Derivative of:
-
(x^2-1)/(x+2)
-
4x
- Sum of series:
- 4x
- Integral of d{x}:
-
4x
-
Identical expressions
- (x^ two - one)/(x+ two)=4x
- (x squared minus 1) divide by (x plus 2) equally 4x
- (x to the power of two minus one) divide by (x plus two) equally 4x
- (x2-1)/(x+2)=4x
- x2-1/x+2=4x
- (x²-1)/(x+2)=4x
- (x to the power of 2-1)/(x+2)=4x
- x^2-1/x+2=4x
- (x^2-1) divide by (x+2)=4x
-
Similar expressions
- sqrt(x^3-4*x^2-10*x+29)=3-x
- (x-7)(x-4)(x-6)=(x-7)(x-3)(x-6)
- (x^2+1)/(x+2)=4x
- (x^2-1)/(x-2)=4x
(x^2-1)/(x+2)=4x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{x^{2} - 1}{x + 2} = 4 x$$
Multiply the equation sides by the denominators:
2 + x
we get:
$$\frac{\left(x + 2\right) \left(x^{2} - 1\right)}{x + 2} = 4 x \left(x + 2\right)$$
$$x^{2} - 1 = 4 x \left(x + 2\right)$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 1 = 4 x \left(x + 2\right)$$
to
$$- 3 x^{2} - 8 x - 1 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -3$$
$$b = -8$$
$$c = -1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{4}{3} - \frac{\sqrt{13}}{3}$$
$$x_{2} = - \frac{4}{3} + \frac{\sqrt{13}}{3}$$
$$\frac{x^{2} - 1}{x + 2} = 4 x$$
Multiply the equation sides by the denominators:
2 + x
we get:
$$\frac{\left(x + 2\right) \left(x^{2} - 1\right)}{x + 2} = 4 x \left(x + 2\right)$$
$$x^{2} - 1 = 4 x \left(x + 2\right)$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 1 = 4 x \left(x + 2\right)$$
to
$$- 3 x^{2} - 8 x - 1 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -3$$
$$b = -8$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (-3) * (-1) = 52
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{4}{3} - \frac{\sqrt{13}}{3}$$
$$x_{2} = - \frac{4}{3} + \frac{\sqrt{13}}{3}$$
Rapid solution
[src]
____
4 \/ 13
x1 = - - - ------
3 3
$$x_{1} = - \frac{4}{3} - \frac{\sqrt{13}}{3}$$
____
4 \/ 13
x2 = - - + ------
3 3
$$x_{2} = - \frac{4}{3} + \frac{\sqrt{13}}{3}$$
x2 = -4/3 + sqrt(13)/3
Sum and product of roots
[src]
sum
____ ____ 4 \/ 13 4 \/ 13 - - - ------ + - - + ------ 3 3 3 3
$$\left(- \frac{4}{3} - \frac{\sqrt{13}}{3}\right) + \left(- \frac{4}{3} + \frac{\sqrt{13}}{3}\right)$$
=
-8/3
$$- \frac{8}{3}$$
product
/ ____\ / ____\ | 4 \/ 13 | | 4 \/ 13 | |- - - ------|*|- - + ------| \ 3 3 / \ 3 3 /
$$\left(- \frac{4}{3} - \frac{\sqrt{13}}{3}\right) \left(- \frac{4}{3} + \frac{\sqrt{13}}{3}\right)$$
=
1/3
$$\frac{1}{3}$$
1/3
The graph