SOLUTION: {{{4/x}}}+{{{4/(2 x+3)}}}=9 A) -{{{5/6}}} B) {{{1/3}}} C) {{{1/2}}} D) {{{11/6}}}

Algebra ->  Trigonometry-basics -> SOLUTION: {{{4/x}}}+{{{4/(2 x+3)}}}=9 A) -{{{5/6}}} B) {{{1/3}}} C) {{{1/2}}} D) {{{11/6}}}      Log On


   

Question 1115184: 4%2Fx+4%2F%282+x%2B3%29=9
A) -5%2F6
B) 1%2F3
C) 1%2F2
D) 11%2F6
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
If you find no special arithmetic tricks to pick one of the options, then solve the actual equation. Start by multiplying both sides by x(2x+3) and simplify,...

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply everything by x(2x+3)
4(2x+3)+4x=9(2x^2+3x)
18^2+27x-12x-12=0
18x^2+15x-12=0
3(6x^2+5x-4)=0
x2+5x-24
(x+8)(x-3)
Divide by 6 and reduce
(x+(8/6)0 or (x+(4/3)) and (x-(3/6)) or (x-(1/2))
factors are (3x+4)(2x-1)=0
x=-4/3, or (1/2); both roots work
C is the best answer.
graph%28300%2C300%2C-5%2C5%2C-10%2C10%2C6x%5E2%2B5x-4%29