Question

What is the solution to the rational equation 4/3 + 3/ x+5 = 21/ 3x+15 ? someone please help

Answer 1

\[\left( 4 \over 3 \right)+\left( 3 \over x+5 \right)=\left( 21 \over 3x+5 \right)\]
what would be the common denominators for all three terms in the equation.

Answer 2

there isnt one

Answer 3

Sorry. I made a typo on the equation.\[\left( 4 \over 3 \right)+\left( 3 \over x+5 \right)=\left( 21\over 3x +15 \right)\]

Answer 4

Common denominator?

Answer 5

3

Answer 6

Close. Hint: 3x+15 can be factored.

Answer 7

x+5

Answer 8

Close. If you have an equation\[\left( 1\over a \right) + \left( 1 \over b \right)=\left( 1 \over ab \right)\]what would be the common denominator

Answer 9

ab

Answer 10

Right, you have the same thing here. a is like 3 and b is like x+5. So what is the common denominator of your equation?

Answer 11

3x+5

Answer 12

Close. It would be 3(x+5)=3x+15

Answer 13

ok

Answer 14

So you need to get each term to be over the common denominator. We multiply the first term by x+5/x+5 to get\[\left( 4 \over 3 \right)\left( x+5 \over x+5 \right)=?\]

Answer 15

4(x+5) / 3(x+5)

Answer 16

So what would you multiply the second term by to get the common denominator?

Answer 17

4?

Answer 18

You want to end up with a term that has the common denominator on the bottom 3(x+5) so you would multiply by 3/3
\[\left( 3 \over x+5 \right)\left( 3 \over 3 \right)=?\]

Answer 19

9/ 3x+5

Answer 20

9/3(x+5)so now our equation looks like\[\left( 4(x+5)+9 \over 3 (x+5) \right)=\left( 21 \over 3 (x+5) \right)\] Can you rearrange and solve for x?