# How do you simplify #(x^2-x-12)/(x^2-11x+30)-(x-4)/(18-x)#?

It can be factored into:

I'm not sure how you are wanting this to simplify, but this should get you going. If this expression was equal to zero, you could add the second fraction to both sides and then divide by common factors (such as (x-4)).

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

To simplify the expression (x^2-x-12)/(x^2-11x+30)-(x-4)/(18-x), we first factor the denominators and combine the fractions with a common denominator.

The denominator x^2-11x+30 can be factored as (x-6)(x-5), and the denominator 18-x can be rewritten as -(x-18).

Now, we can rewrite the expression as follows:

(x^2-x-12)/[(x-6)(x-5)] - (x-4)/[-(x-18)]

To combine the fractions, we need to find a common denominator, which is (x-6)(x-5)(x-18).

Multiplying the first fraction by (x-18)/(x-18) and the second fraction by (x-5)/(x-5), we get:

[(x^2-x-12)(x-18)]/[(x-6)(x-5)(x-18)] - [(x-4)(x-5)]/[(x-6)(x-5)(x-18)]

Expanding and simplifying the numerators, we have:

[(x^3-19x^2+90x+12x^2-216x+1296) - (x^2-9x+20)]/[(x-6)(x-5)(x-18)]

Combining like terms in the numerator, we get:

(x^3-7x^2-125x+1276)/[(x-6)(x-5)(x-18)]

Therefore, the simplified expression is (x^3-7x^2-125x+1276)/[(x-6)(x-5)(x-18)].

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.

- How do you simplify #(6m+6n) / 2#?
- How do you divide #(-x^4+5x^3-5x^2-6x-2)/(x^2-4) #?
- Using long division solve #(12x^2+9x-7)-:3x#?
- Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?
- If x varies inversely as y and y=40 when x=4, how do you find x when y=20?

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