Home > Algebra > Clearing Denominators in Rational Equations

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

Answer 1

Nathan Axel

Cross multiplication is used here:

# (x-2) xx x = 1 xx 3#

we obtain equation: # x^2 - 2x = 3# # x^2 - 2x - 3 = 0#

solving this equation by grouping / splitting the middle term: # x^2 - 2x - 3 = 0#

The middle term # -2x = - 3x + 1x # and The product # -3 = -3 xx 1#.

# x^2 - 3x + 1x - 3 = 0# grouping by taking out common terms: # x( x - 3) +1 (x - 3) = 0# # (x - 3) + (x+1) = 0#

solutions for the equation: # x = 3 or x = -1#

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

Answer 2

Savannah Anderson

To solve the equation (x-2)/3 = 1/x, we can start by cross-multiplying. This means multiplying the numerator of the first fraction (x-2) by the denominator of the second fraction (x), and multiplying the denominator of the first fraction (3) by the numerator of the second fraction (1). This gives us (x-2) * x = 3 * 1. Simplifying further, we have x^2 - 2x = 3. Rearranging the equation, we get x^2 - 2x - 3 = 0. To solve this quadratic equation, we can factor it as (x-3)(x+1) = 0. Therefore, x can be either 3 or -1.

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

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.