Answer:

[tex]f(g(-5)) = \frac{3}{2}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{2x}{3x+5}[/tex]

[tex]g(x) = \frac{3}{x+4}[/tex]

Required

Find f(g(-5))

First, we calculate f(g(x))

[tex]f(x) = \frac{2x}{3x+5}[/tex]

Substitute g(x) for x

[tex]f(g(x)) = \frac{2g(x)}{3g(x) + 5}[/tex]

Substitute [tex]\frac{3}{x+4}[/tex] for g(x)

[tex]f(g(x)) = \frac{2*\frac{3}{x+4}}{3*\frac{3}{x+4} + 5}[/tex]

[tex]f(g(x)) = \frac{\frac{6}{x+4}}{\frac{9}{x+4} + 5}[/tex]

[tex]f(g(x)) = \frac{6}{x+4}/ (\frac{9}{x+4} + 5})[/tex]

Take LCM

[tex]f(g(x)) = \frac{6}{x+4}/ \frac{9+5x+20}{x+4}}[/tex]

[tex]f(g(x)) = \frac{6}{x+4}/ \frac{5x+29}{x+4}}[/tex]

Rewrite as multiplication

[tex]f(g(x)) = \frac{6}{x+4}* \frac{x+4}{5x+29}}[/tex]

[tex]f(g(x)) = \frac{6}{5x+29}[/tex]

Substitute -5 for x

[tex]f(g(-5)) = \frac{6}{-5*5+29}[/tex]

[tex]f(g(-5)) = \frac{6}{-25+29}[/tex]

[tex]f(g(-5)) = \frac{6}{4}[/tex]

[tex]f(g(-5)) = \frac{3}{2}[/tex]

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