I am having trouble with this problem: 1+(1/x)= 12/x^2.?

Question

Can someone please help me and try and explain how you do it??

Answer 1

Let y = 1/x

So you have 1 + y - 12y^2 = 0
Now solve the quadratic to get
y = -1/4, 1/3
So x = -4, 3

Answer 2

OK, you need to solve for x.

So you'll need to unwind the nasty problem.

Step 1: get the x's on one side. I'll choose getting them on the left side.
Multiply both sides by (x^2) which will cancel out the x^2 in the denominator on the right. You'll be left with:
(x^2)(1+(1/x)) = 12

Step 2: Simplify by multiplying through on the left.
(x^2) + (x^2)(1/x) = 12
(x^2) + (x^2/x) = 12
(x^2) + ( [x * x] / x) = 12
(x^2) + x = 12

Step 3: Put in standard form of ax^2 + bx + c = 0
x^2 + x - 12 = 0

Step 4: Use the quadratic equation or complete the square to find the roots of the equation:

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

So x = -4 or x = 3.

Check your answer:

1 + (1/3) = 12 / (3^2) << substitute 3 for x >>
1 + 1/3 = 12 / 9 << multiply through by 9>>
9 + 3 = 12 << looks right to me >>

1 + (1/-4) = 12 / (-4 ^ 2)
1 - 1/4 = 12 / 16
16 - 4 = 12 << checks again >>

You're done!

Answer 3

1 + 1/x = 12/x^2
Multiply through by x^2 (noting that we must not allow x=0 as a final answer):
x^2 + x = 12
=> x^2 + x - 12 = 0
=> (x-3)(x+4) = 0
=> x = 3 or -4.

Answer 4

1 + (1/x) = 12/(x^2)

To get rid of all fractions, multiply by the LCD of all numbers. In this case, it's x^2. Multiply both sides by x^2 to get

x^2 [1 + (1/x)] = x^2 [12/x^2]
x^2 + x = 12
x^2 + x - 12 = 0
(x + 4)(x - 3) = 0

Therefore,

x = {-4, 3}

Answer 5

1 + 1/x = 12/x^2


Multiply both sides by x^2

x^2 + 1x = 12

x^2 + 1x - 12 = 0

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

x = 3

x = -4

I Think I Gave You The Answer LOL
Good Luck :) Hope It Helps

Answer 6

x + 1 = 12/x
x^2 + x = 12
x^2 + x - 12 = 0
(x + 4)(x - 3) = 0

x + 4 = 0, & x - 3 = 0

x = -4 & 3

Answer 7

1+(1/x)=12/x^2

Multiplu both sides of the equation by x^2

x^2+x = 12
x^2+x-12=0
x^2+4x-3x-12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0

x=-4 or x=3

Answer 8

1+(1/x)=12/x^2
first i would multiply the x^2 to both sides, making the equation x^2 + x (the x's cancel) = 12
complete the square and solve

Answer 9

Make it look like a quadratic equation by getting all terma on on side to equal zero...
x^2(1+1/x)=12
x^2+x-12=0

no apply quadratice formula...
x=(-b)+/-(sqrt(b^2-4ac)))/2a
x=(-1+/-(sqrt(1+48)))/2
x=(-1+/-7)/2
x=3,-4

Answer 10

i got x = -4 or 3