Question

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

Answer 1

4/3+3/x+5 = 21/3x + 15
4/3+5 + 3/x = 7/x + 15
4/3+5-15 = 7/x+3/x
-8 - 2/3 = 10/x
x = 10/(-8-2/3)

Answer 2

\[4/3+3/x+5=21/3x+15\]
First you simplify the equation by combining like terms and simplifying fractions:
\[6 \frac{1}{3} +\frac{3}{x}=\frac{7}{x}+15\]
Then you use the subtraction property of equality and subtract \[(\frac{3}{x}+15)\]from both sides and get:
\[-8\frac{1}{3}=\frac{4}{x}\]
When you multiply both sides by x you get:
\[-\frac{25}{3}x=4\]
Divide both sides by the coefficient of x to get that \[x=\frac{12}{25}\] :)

Answer 3

4/3 + 3/(x+5) =21/(3x+15)
4(x+5)+9 21
--------- = ---------
3(x+5) 3(x+5)

4x+20+9=21
4x+29=21
4x=21-29
4x=-8
x=-8/4
x=-2