Algebraic expressions are expressions that use literals (i.e alphabets) to represent its variables.
- The rational expressions are: [tex]\frac{2}{3x}[/tex] and [tex]\frac{x^2 - 4}{x - 2}[/tex].
- The simplified expressions are: [tex]2m[/tex], [tex]a[/tex] and [tex]\frac 1{x - 5}[/tex]
(a) Encircle Rational Algebraic Expressions
A rational algebraic expression is a ratio of two polynomials.
So, the rational expressions are:
[tex]\frac{2}{3x}[/tex] and [tex]\frac{x^2 - 4}{x - 2}[/tex] because the numerator and the denominator are polynomials
However,
[tex]6x - 1[/tex], [tex]x^2 + x - 3[/tex] and [tex]\frac{1}{x^{-5}}[/tex] are not rational
(b) Simplify
[tex]\frac{4m^2}{2m}[/tex]
Expand the numerator
[tex]\frac{4m^2}{2m} = \frac{2m \times 2m}{2m}[/tex]
Cancel out 2m
[tex]\frac{4m^2}{2m} = 2m[/tex]
[tex]\frac{abc}{bc}[/tex]
Expand the numerator
[tex]\frac{abc}{bc} = \frac{a \times bc}{bc}[/tex]
Cancel out bc
[tex]\frac{abc}{bc} = a[/tex]
[tex]\frac{x + 1}{x^2 - 4x - 5}[/tex]
Expand the denominator
[tex]\frac{x + 1}{x^2 - 4x - 5} = \frac{x + 1}{x^2 - 5x + x - 5}[/tex]
Factorize
[tex]\frac{x + 1}{x^2 - 4x - 5} = \frac{x + 1}{x(x - 5) + 1(x - 5)}[/tex]
Factor out x - 5
[tex]\frac{x + 1}{x^2 - 4x - 5} = \frac{x + 1}{(x + 1)(x - 5)}[/tex]
Cancel out the common factor
[tex]\frac{x + 1}{x^2 - 4x - 5} = \frac{1}{x - 5}[/tex]
Read more about algebraic expressions at:
https://brainly.com/question/11227332
