The function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is a rational function
The simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is [tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
The function expression is given as:
f(x) =x - 4/x^2 + 13x + 36
Rewrite properly as:
[tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex]
Expand the denominator
[tex]f(x) =\frac{x - 4}{x^2 + 4x + 9x + 36}[/tex]
Factorize the denominator
[tex]f(x) =\frac{x - 4}{x(x + 4) + 9(x + 4)}[/tex]
Factor out x + 9
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
Hence, the simplified expression of the function [tex]f(x) =\frac{x - 4}{x^2 + 13x + 36}[/tex] is
[tex]f(x) =\frac{x - 4}{(x + 9)(x + 4)}[/tex]
Read more about rational functions at:
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