Mister Exam

Other calculators

(x^2-1)/(x+2)=4x

(x^2-1)/(x+2)=4x equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
 2          
x  - 1      
------ = 4*x
x + 2
x2−1x+2=4x\frac{x^{2} - 1}{x + 2} = 4 x
Simplify
Detail solution
Given the equation:
x2−1x+2=4x\frac{x^{2} - 1}{x + 2} = 4 x
Multiply the equation sides by the denominators:
2 + x
we get:
(x+2)(x2−1)x+2=4x(x+2)\frac{\left(x + 2\right) \left(x^{2} - 1\right)}{x + 2} = 4 x \left(x + 2\right)
x2−1=4x(x+2)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
x2−1=4x(x+2)x^{2} - 1 = 4 x \left(x + 2\right)
to
−3x2−8x−1=0- 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=−3a = -3
b=−8b = -8
c=−1c = -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
x1=−43−133x_{1} = - \frac{4}{3} - \frac{\sqrt{13}}{3}
x2=−43+133x_{2} = - \frac{4}{3} + \frac{\sqrt{13}}{3}
The graph
02468-12-10-8-6-4-2-50005000
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
             ____
       4   \/ 13 
x1 = - - - ------
       3     3
x1=−43−133x_{1} = - \frac{4}{3} - \frac{\sqrt{13}}{3} 
             ____
       4   \/ 13 
x2 = - - + ------
       3     3
x2=−43+133x_{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
(−43−133)+(−43+133)\left(- \frac{4}{3} - \frac{\sqrt{13}}{3}\right) + \left(- \frac{4}{3} + \frac{\sqrt{13}}{3}\right) 
=
-8/3
−83- \frac{8}{3} 
product
/        ____\ /        ____\
|  4   \/ 13 | |  4   \/ 13 |
|- - - ------|*|- - + ------|
\  3     3   / \  3     3   /
(−43−133)(−43+133)\left(- \frac{4}{3} - \frac{\sqrt{13}}{3}\right) \left(- \frac{4}{3} + \frac{\sqrt{13}}{3}\right) 
=
1/3
13\frac{1}{3} 
1/3
Numerical answer [src] 
x1 = -2.535183758488
x2 = -0.13148290817867
x2 = -0.13148290817867
The graph
(x^2-1)/(x+2)=4x equation
    © Mister Exam – Calculator