Mathematics: 2. Add: Simplify and state the domain.

2. Add: Simplify and state the domain. - id214276948, corey36dylon

krlx

08.09.2021

see explanation

Step-by-step explanation:

$\frac{3}{5x+10}$ + $\frac{2x}{x^2-2x-8}$ ← factor the denominators

= $\frac{3}{5(x+2)}$ + $\frac{2x}{(x-4)(x+2)}$

= $\frac{3(x-4)}{5(x+2)(x-4)}$ + $\frac{2x(5)}{5(x+2)(x-4)}$ ← simplify numerator

= $\frac{3x-12+10x}{5(x+2)(x-4)}$

= $\frac{13x-12}{5(x+2)(x-4)}$

The denominator cannot be zero as this would make the rational function undefined

Equating the denominator to zero and solving gives the values of x that cannot be in the domain

5(x + 2)(x - 4) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 4 = 0 ⇒ x = 4

x = - 2, x = 4 ← excluded values

domain : x ∈ R ( x ≠ - 2, x ≠ 4 )

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almostnevercbbc

02.06.2022

150 Square Units

Step-by-step explanation:

(Sorry if I become confusing)

The base of the triangles is 10 units.

The height of the triangles is 15 units.

The formula I used was A= $\frac{1}{2}bh$

b=base and h=height A=area

A= $\frac{1}{2}(10)(15)$

A= $\frac{1}{2}(10)(15)$ =75

A=75

Multiply by two to get the area for both triangles.

75·2=150

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