Rational algebraic expressions are expressions that can be represented as a quotient of two polynomials.
The result of the expressions are:
[tex]\mathbf{\frac{5x}{3x - 9} = \frac{20}{3}}[/tex]
[tex]\mathbf{\frac{y^2 + 4y + 1}{y^2- 1} = -1}[/tex]
[tex]\mathbf{(a)\ \frac{5x}{3x - 9};\ x = 4}[/tex]
First, we substitute 4 for x
[tex]\mathbf{\frac{5x}{3x - 9} = \frac{5 \times 4}{3 \times 4 - 9}}[/tex]
Evaluate all products
[tex]\mathbf{\frac{5x}{3x - 9} = \frac{20}{12 - 9}}[/tex]
Subtract
[tex]\mathbf{\frac{5x}{3x - 9} = \frac{20}{3}}[/tex]
[tex]\mathbf{(b)\ \frac{y^2 + 4y + 1}{y^2- 1};\ y =-2}[/tex]
First, we substitute -2 for y
[tex]\mathbf{\frac{y^2 + 4y + 1}{y^2- 1} = \frac{(-2)^2 + 4 \times (-2) + 1}{(-2)^2- 1}}[/tex]
Evaluate all products and exponents
[tex]\mathbf{\frac{y^2 + 4y + 1}{y^2- 1} = \frac{4 -8 + 1}{4- 1}}[/tex]
Subtract
[tex]\mathbf{\frac{y^2 + 4y + 1}{y^2- 1} = \frac{-3}{3}}[/tex]
[tex]\mathbf{\frac{y^2 + 4y + 1}{y^2- 1} = -1}[/tex]
Read more about rational algebraic expressions at:
https://brainly.com/question/21511236
