# How do you simplify #(x^2 - 16 )/( 2x^2 - 9x + 4) div (2x^2 + 14x + 24) /( 4x + 4)#?

By factoring note that:

Cancel like terms:

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

To simplify the expression, we can start by factoring the numerator and denominator of the first fraction:

(x^2 - 16) = (x - 4)(x + 4) (2x^2 - 9x + 4) = (2x - 1)(x - 4)

Next, we can factor the numerator and denominator of the second fraction:

(2x^2 + 14x + 24) = 2(x^2 + 7x + 12) = 2(x + 3)(x + 4) (4x + 4) = 4(x + 1)

Now, we can rewrite the expression as a division of fractions:

[(x - 4)(x + 4)] / [(2x - 1)(x - 4)] ÷ [(2(x + 3)(x + 4)) / (4(x + 1))]

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:

[(x - 4)(x + 4)] / [(2x - 1)(x - 4)] * [(4(x + 1)) / (2(x + 3)(x + 4))]

Next, we can cancel out common factors:

[(x - 4)(x + 4)] / [(2x - 1)(x - 4)] * [(4(x + 1)) / (2(x + 3)(x + 4))] = [(x - 4) / (2x - 1)] * [(4(x + 1)) / (2(x + 3))]

Finally, we can simplify further by canceling out common factors:

[(x - 4) / (2x - 1)] * [(4(x + 1)) / (2(x + 3))] = [(x - 4)(x + 1)] / [(2x - 1)(x + 3)]

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

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.

- R is inversely proportional to the cube of S, if R = 2 and S = 7, how do you find the value of k?
- How do you solve #-4p - 9= - 17- 3p#?
- How do you graph #f(x)=x/(x^2-1)# using holes, vertical and horizontal asymptotes, x and y intercepts?
- How do you solve #10/14=30/m#?
- How do you simplify #(10y-30)/(y^2-1)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7