Solving rational equation..please help!!!?

Question

Solve the equation, and check solution:

_x+10__ = __4_

(x^2 - 2)------ ( x)

THE SPACE BETWEEN THE TWO DENOMINATORS WAS FILLED WITH THAT LINE BECAUSE I COULD NOT WRITE IT CORRECTLY OTHERWISE BECAUSE THE X KEPT MOVING SO THAT HAS NOTHING TO DO WITH THE PROBLEM...

THANK YOU!!

Answer 1

its either 4 or (-2/3). Its a quadratic equation. So first, multiply (x^2-2) and (x) to both sides of the equation. This step will eliminate the denominators. After doing that and simplifying, you will get [3x^2 -10x - 8 = 0]. Solve the quadratic equation, any method (I prefer to factor the equation). Then, u will get the 4 and [-2/3].

Answer 2

(x + 10) / (x^2 - 2) = 4 / x

Cross multiply....

x(x + 10) = 4(x^2 - 2)

x^2 + 10x = 4x^2 - 8

0 = 3x^2 - 10x - 8

0 = (3x + 2)(x - 4)

x = -2/3 or 4

You can check it yourself.  (Check by plugging in the value for x and see if you have a true statement.)

Answer 3

_x+10__ = __4_

(x^2 - 2)------ ( x)

(x)(x+10) = (4)(x^2-2)

x^2+10x = 4x^2-8

3x^2-10x-8=0

(3x+2) (x-4)

x = -2/3 and 4

Answer 4

(x+10)/(x^2 - 2) = 4/x

Is that correct?

Multiply each side by x^2 - 2

(x + 10) = 4(x^2 - 2)/x

Multiply each side by x

x(x+10) = 4(x^2 - 2)

Distribute through the parentheses

x^2 + 10x = 4x^2 - 8

Subtract (x^2 + 10x) from each side

0 = 3x^2 - 10x - 8

Factor (or use the quadratic formula)

0 = (3x +2)(x - 4)

By the zero property,

3x + 2 = 0 or x - 4 = 0

So

x = -2/3 or x = 4

Check the original equation to verify.

Answer 5

Cross-multiply, collect terms, and solve.

4(x^2 - 2) = x(x + 10)

4x^2 - 8 = x^2 + 10x

3x^2 - 10x - 8 = 0

(3x + 2)(x - 4) = 0 . . .

Solve it yourself from here, and check your answers against the original fractions.  Note that a solution value of 0 or sqrt(2) would be invalid because of the denominators of the original fractions, but neither value works out as a solution so that's not a problem.

Answer 6

Cross multiply.

x(x + 10) = 4(x^2 - 2)

x^2 + 10x = 4x^2 - 8

0 = 3x^2 - 10x - 8

0 = 3x^2 + 2x - 12x - 8

0 = x(3x + 2) - 4(3x - 2)

0 = (x - 4)(3x + 2)

x - 4 = 0 AND 3x + 2 = 0

x = 4 AND x = -2/3

Check:

(4+10)/(4^2 - 2) = 4/4

14/14 = 4/4

1 = 1

(10 - 2/3)/((-2/3)^2 - 2) = 4/(-2/3)

(28/3)/(-14/9) = 4(-3/2)

(28/3)(-9/14) = -6

-6 = -6

There ya go.