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dannielle
What is the solution to the rational equation 4/3+3/x+5=21/3x+15 ?
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)
\[4/3+3/x+5=21/3x+15\] 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 \[x=\frac{12}{25}\] :)
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