Simplifying rational expressions
x^2-16/x^2+6x+8 = x-4/x+2
x^2-x-6/x^2-3x-10 = x-3/x-5

1)

Decompose the numerator and denominator into multipliers

To simplify the numerator we use the formula of difference of squares

To decompose the denominator into multipliers solve the square equation

Formula for factoring a square equation

Substituting the found roots of the equation into the formula

After simplifying the numerator and denominator we get a fraction

, so

2)

Decompose the numerator and denominator into multipliers

To decompose the numerator into multipliers solve the square equation

Formula for factoring a square equation

Substituting the found roots of the equation into the formula

To decompose the denominator into multipliers solve the square equation

Formula for factoring a square equation

Substituting the found roots of the equation into the formula

After simplifying the numerator and denominator we get a fraction

, so

Hello from Russia:^)

Answers are:

x-4/x+2

x-3/x-5

Step-by-step explanation:

a. the residual plot for model 1 has a random pattern and is a good fit for the data.