Question

Solve the rational equation: 2-4/x^2=-2/x

Answer 1

Try the method of cross-multiplication first.\[\huge \frac{a}{b}=\frac{c}{d}\ \Rightarrow \ ad=bc\]

Answer 2

@dpaInc

Answer 3

@jim_thompson5910

Answer 4

is the equation \[\Large 2 - \frac{4}{x^2}=-\frac{2}{x}\] ?

Answer 5

Yes =)

Answer 6

alright great, the first thing we do is get rid of the fractions

Answer 7

we do this by multiplying every term by the LCD x^2

Answer 8

So multiply that first term 2 by x^2 to get 2x^2

Then multiply -4/x^2 by x^2 to get x^2*(-4/x^2) = -4

Finally, multiply -2/x by x^2 to get x^2(-2/x) = -2x^2/x = -2x


So

2-4/x^2=-2/x

turns into

2x^2 - 4 = -2x

Answer 9

What's next from here?

Answer 10

Then would I get: 4x-4=-2x

Answer 11

No, 2x^2 is not the same as 4x

Answer 12

Okay, can you explain how I could get x alone?

Answer 13

sure thing

Answer 14

First get the expression into standard form


2x^2 - 4 = -2x


2x^2 - 4 + 2x = 0


2x^2 + 2x - 4 = 0


Now use the quadratic formula to solve for x.


x = (-b+-sqrt(b^2-4ac))/(2a)


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


x = (-2+-sqrt(4-(-32)))/(4)


x = (-2+-sqrt(36))/4


x = (-2+sqrt(36))/4 or x = (-2-sqrt(36))/4


x = (-2+6)/4 or x = (-2-6)/4


x = 4/4 or x = -8/4


x = 1 or x = -2


So the solutions are x = 1 or x = -2

Answer 15

Thank you!! =)

Answer 16

yw