How do you solve #(x - 2)/ 3 = 1/ x#?

Answer 1

#x=3# or #x=-1#.

Multiply Crosswise:

#(x-2)/3=1/x#
#x(x-2)=3#
Expand: #x(x-2)=3# #x^2-2x=3# #x^2-2x-3=0#

This leaves us with a quadratic equation, which we can further factor:

#(x-3)(x+1)=0#

Using the null factor law, we can now solve the following by figuring out the numbers that cause each bracket to equal zero:

#(x-3)(x+1)=0#
Solution 1: #color(red)((3-3))(3+1)=0# #0*4=0# #0=0# Therefore, one solution to the equation is #x=3#
Solution 2: #(1-3)color(red)((-1+1))=0# #-2*0=0# #0=0# Therefore, the other solution to the equation is #x-1#
Therefore, #x=3# or #x=-1#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the equation (x - 2)/3 = 1/x, we can start by cross-multiplying to eliminate the fractions. This gives us (x - 2) * x = 3 * 1. Expanding the left side of the equation, we have x^2 - 2x = 3. Rearranging the equation, we get x^2 - 2x - 3 = 0. This is a quadratic equation, which can be factored as (x - 3)(x + 1) = 0. Setting each factor equal to zero, we find x = 3 or x = -1. Therefore, the solutions to the equation are x = 3 and x = -1.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7