Solve the quadratic function

x+5/3x+2-4-2x/3x^2+8x+4=x+4/x+2

Question

Solve the quadratic function

x+5/3x+2-4-2x/3x^2+8x+4=x+4/x+2

anonymous · Answer

Okay so i already i already know to factor the 3x^2 part, and then find the LCD, but my end answer isn't corresponding with the book and i have no idea how to do it. HELP

campbell_st · Answer

do some factorising 

$$\frac{x+5}{3x+2} - \frac{2(2-x)}{(x+2)(3x+2)} = \frac{x+4}{x+2}$$

the common denominator is (x+2)(3x+2)

the getting everything over a common denominator

$$\frac{(x+5)(x+2)-(x-2)}{(3x+2)(x+2)} =\frac{(x+4)(3x+2)}{(3x+2)(x+2)}$$

I'd expand and simplify the numerators

$$\frac{x^2 + 7x + 10 -4+2x}{(3x+2)(x+2)}  = \frac{(x+4)(x+2)}{(3x+2)(x+2)}$$