Question

can someone help me with the steps on how to solve the following proportion and solve for x?

Answer 1

Sure

Answer 2

\[\frac{ 12 }{ x+3 }=\frac{ x+3 }{ x}\]

Answer 3

is there an answer choice

Answer 4

no, i had to set up a proportion to find the sides of similar right triangles and i got that, but i forgot how to actually solve the proportion haha.

Answer 5

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
x+3/x=12/x+3

Answer 6

Set up the rational expression with the same denominator over the entire equation.

Answer 7

then we multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of x(x+3). The (x+3)/x expression needs to be multiplied by (x+3)/(x+3) to make the denominator x(x+3). The 12/(x+3) expression needs to be multiplied by (x)/(x) to make the denominator x(x+3).

x+3/x⋅x+3/x+3=12/x+3⋅x/x

Answer 8

wouldn't you have to cross multiply?

Answer 9

i dont do mines that way but u can idk if it works

Answer 10

because thats how my teacher told us to do it. so in that case it would be \[12x=x ^{2}+9\] is that right?

Answer 11

what i got 3

Answer 12

i know the answer is 3, but idk how to get that.

Answer 13

ok let me finsh

Answer 14

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of x(x+3).

(x+3)(x+3)x/(x+3)=12/x+3⋅x/x

Answer 15

i can't see what your typing, a bunch of diamonds with ? in them are showing up

Answer 16

it changed u see it

Answer 17

Apply the distributive property.

x(x+3)+3(x+3)/x(x+3)=12/x+3⋅x/x

Answer 18

Apply the distributive property.

x(x)+x(3)+3(x+3)/x(x+3)=12/x+3⋅x/x

Answer 19

Apply the distributive property.

x(x)+x(3)+3(x)+3(3)/x(x+3)=12/x+3⋅x/x

Multiply x by x to get x2.

x2+x(3)+3(x)+3(3)/x(x+3)=12/x+3⋅x/x

Answer 20

Multiply x by 3 to get x⋅3.

x2+x⋅3+3(x)+3(3)/x(x+3)=12/x+3⋅x/x

Move 3 to the left of the expression x⋅3.

x2+3⋅x+3(x)+3(3)/x(x+3)=12/x+3⋅x/x

Multiply 3 by x to get 3x.

x2+3x+3(x)+3(3)/x(x+3)=12/x+3⋅x/x

Answer 21

ohhh ok i got it thanks!

Answer 22

You're Welcome