Question

Solve the equation. Check the solution. g+4/g-2 = g-5/g-8

Answer 1

(g + 4)/(g - 2) = (g - 5)/(g - 8)
cross multiply
(g + 4)(g - 8) = (g - 5)(g - 2)
expand
g^2 - 4g - 32 = g^2 - 7g + 10
- g^2
-4g - 32 = -7g + 10
+ 7g
3g - 32 = 10
+ 32
3g = 42
÷ 3
g = 14

I hope this helps!

Answer 2

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.