(x-9)/(x+4)=3?

Math

2 Answers
Apr 26, 2018

x=-21/2

Explanation:

(x-9)/(x+4)=3 /*(x+4) to get rid of the fraction

x-9=3*(x+4)

x-9=3x+12

x-3x=12+9

-2x=21 /*(-1)

2x=-21

x=-21/2

Apr 26, 2018

x = -21/2

Explanation:

We must begin by adding the domain restriction x!=-4 because this would cause division by 0:

(x-9)/(x+4)=3, x !=-4

Now that we have assured that we are not inadvertently multiplying by 0, we can eliminate the denominator by multiplying both sides by (x+4):

x-9=3(x+4), x !=-4

Use the distributive property:

x-9=3x+12, x !=-4

Add 9-3x to both sides:

-2x = 21, x!=-4

We can drop the domain restriction because it is obvious that the solution will not violate it:

-2x = 21

Multiply both sides by -1/2:

x = -21/2