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2 years ago

Find the LCD of the given rational equation: -3/x+2 + 5x/x-1 = x+2/x^2-3x+2

1 answer:

5 0

Answer:

(x - 1)( x - 2) (x + 2) = x³ -x² -4x + 4.

Explanation:

1) Given equation:

3 5x x + 2
- ------- + -------- = ---------------
x + 2 x - 1 x² - 3x + 2

2) So, the denominators are x + 2, x - 1, and x² - 3x + 2

3) The LCD is the product of the common and non common factors raised to the greatest power.

4) x + 2, and x - 1 are already prime factors

5) Factor x² - 3x + 2

x² - 3x + 2 = (x - 2)(x - 1)

6) Then, the factors are x + 2, x - 1, and x - 2, and the LCD is the product of them:
(x - 1)( x - 2) (x + 2)

7) If you expand the products (distributive property) you get:
x³ -x² -4x + 4.

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Read 2 more answers

Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

$h=\frac{-b}{2a}$

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: $y=a(x-h)^{2} +k$

a: 1

h: 3

k: -25

$y=(x-3)^{2} -25$

Hope this helps!

3 0

2 years ago