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