Home > Algebra > Excluded Values for Rational Expressions

How do you simplify and find the restrictions for #(2x^2-4x )/(3x)#?

Answer 1

See a solution process below:

First, we can rewrite this expression as:

#(2x^2)/(3x) - (4x)/(3x) => (2 * x * x)/(3x) - (4color(red)(cancel(color(black)(x))))/(3color(red)(cancel(color(black)(x)))) =>#

#(2 * color(red)(cancel(color(black)(x))) * x)/(3color(red)(cancel(color(black)(x)))) - 4/3 =>#

#(2x)/3 - 4/3#

Where

#3x != 0# or #x != 0#

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

Answer 2

Genesis Allen

To simplify the expression (2x^2-4x)/(3x), we can factor out the common term of x from the numerator. This gives us x(2x-4)/(3x).

Next, we can simplify further by canceling out the common factor of x in the numerator and denominator. This leaves us with (2x-4)/3.

To find the restrictions, we need to identify any values of x that would make the denominator equal to zero. In this case, the denominator is 3x, so the restriction is x ≠ 0.

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.