# Solve for g (g-2)/(g+10)=(g-4)/(g+5)

g-2g+10=g-4g+5
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
(g-2)⋅(g+5)=(g+10)⋅(g-4)
Solve the equation for g.
Simplify (g-2)⋅(g+5).
Expand (g-2)(g+5) using the FOIL Method.
Apply the distributive property.
g(g+5)-2(g+5)=(g+10)⋅(g-4)
Apply the distributive property.
g⋅g+g⋅5-2(g+5)=(g+10)⋅(g-4)
Apply the distributive property.
g⋅g+g⋅5-2g-2⋅5=(g+10)⋅(g-4)
g⋅g+g⋅5-2g-2⋅5=(g+10)⋅(g-4)
Simplify and combine like terms.
Simplify each term.
Multiply g by g.
g2+g⋅5-2g-2⋅5=(g+10)⋅(g-4)
Move 5 to the left of g.
g2+5⋅g-2g-2⋅5=(g+10)⋅(g-4)
Multiply -2 by 5.
g2+5g-2g-10=(g+10)⋅(g-4)
g2+5g-2g-10=(g+10)⋅(g-4)
Subtract 2g from 5g.
g2+3g-10=(g+10)⋅(g-4)
g2+3g-10=(g+10)⋅(g-4)
g2+3g-10=(g+10)⋅(g-4)
Simplify (g+10)⋅(g-4).
Expand (g+10)(g-4) using the FOIL Method.
Apply the distributive property.
g2+3g-10=g(g-4)+10(g-4)
Apply the distributive property.
g2+3g-10=g⋅g+g⋅-4+10(g-4)
Apply the distributive property.
g2+3g-10=g⋅g+g⋅-4+10g+10⋅-4
g2+3g-10=g⋅g+g⋅-4+10g+10⋅-4
Simplify and combine like terms.
Simplify each term.
Multiply g by g.
g2+3g-10=g2+g⋅-4+10g+10⋅-4
Move -4 to the left of g.
g2+3g-10=g2-4⋅g+10g+10⋅-4
Multiply 10 by -4.
g2+3g-10=g2-4g+10g-40
g2+3g-10=g2-4g+10g-40
g2+3g-10=g2+6g-40
g2+3g-10=g2+6g-40
g2+3g-10=g2+6g-40
Move all terms containing g to the left side of the equation.
Subtract g2 from both sides of the equation.
g2+3g-10-g2=6g-40
Subtract 6g from both sides of the equation.
g2+3g-10-g2-6g=-40
Combine the opposite terms in g2+3g-10-g2-6g.
Subtract g2 from g2.
3g-10+0-6g=-40
3g-10-6g=-40
3g-10-6g=-40
Subtract 6g from 3g.
-3g-10=-40
-3g-10=-40
Move all terms not containing g to the right side of the equation.
Add 10 to both sides of the equation.
-3g=-40+10
-3g=-30
-3g=-30
Divide each term by -3 and simplify.
Divide each term in -3g=-30 by -3.
-3g-3=-30-3
Cancel the common factor of -3.
Cancel the common factor.
-3g-3=-30-3
Divide g by 1.
g=-30-3
g=-30-3
Divide -30 by -3.
g=10
g=10
g=10
Solve for g (g-2)/(g+10)=(g-4)/(g+5)

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