Question

Solve for x 1. 2x upon x-3+1 upon 2x+3+3x+9upon (x-3)(2x+3)=0;x is not equal to the 3,minus 3 upon 2

Answer 1

Hope this helps you..^_^

Answer 2

Answer:

x = -1

Step-by-step explanation:

 Given: $\frac{2x}{x-3}+\frac{1}{2x+3}+ \frac{3x+9}{(x-3)(2x+3)}=0$

We have to solve for x,

Consider the given expression,

$\frac{2x}{x-3}+\frac{1}{2x+3}+ \frac{3x+9}{(x-3)(2x+3)}=0$

Taking LCM( (x-3), (2x+3), (x-3)(2x+3)) = (x-3)(2x+3)

Thus, expression becomes,

$\frac{2x(2x+3)+(x-3)+3x+9}{(x-3)(2x+3)}=0$

Cross multiply, we have,

$2x(2x+3)+(x-3)+3x+9=(x-3)(2x+3)\times 0$

simplify further, we have,

$4x^2+6x+x-3+3x+9= 0$

$4x^2+10x+6= 0$

taking 2 common, we have,

$2x^2+5x+3= 0$

Solving using middle term splitting method, we have,

5x can be written as 2x + 3x

$2x^2+2x+3x+3= 0$

taking 2x common from first two terms and 3 from last two terms, we have,

$2x(x+1)+3(x+1)= 0$

$(2x+3)(x+1)= 0$

This implies, $(x+1)= 0$ or $(2x+3)= 0$

This implies, $x=-1$ or $x=\frac{-3}{2}$

Since, given $x\neq \frac{-3}{2}$

thus, x = -1