Answer:
Option (d) is correct.
g = 14
Step-by-step explanation:
Given: \(\frac{g+4}{g-2} =\frac{g-5}{g-8}\)
We have to solve for g.
Consider the given expression \(\frac{g+4}{g-2} =\frac{g-5}{g-8}\)
Apply cross multiply rule,
\(if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c\)
We have
\(\left(g+4\right)\left(g-8\right)=\left(g-2\right)\left(g-5\right)\)
Apply distributive rule,
\(\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\)
\(\left(g+4\right)\left(g-8\right)=gg+g\left(-8\right)+4g+4\left(-8\right)\)
Simplify, we get,
\(\left(g+4\right)\left(g-8\right)=g^2-4g-32\)
Similarly, \(\left(g-2\right)\left(g-5\right)=g^2-7g+10\)
Substitute back, we have,
\(g^2-4g-32=g^2-7g+10\)
Simplify, we have,
\(g^2-4g=g^2-7g+42\)
Further simplification give, \(3g=42\)
Divide both side by 3,
We have g = 14
Thus, Option (d) is correct.
