please its my urgent question answer if anyone knows
solve 2 X upon x minus 3 + 1 upon 2 X + 3 + 3 X + 9 upon x minus 3 into 2 X + 3
Answers
Answer:
Answer:x = -1
Answer:x = -1Step-by-step explanation:
Given: \frac{2x}{x-3}+\frac{1}{2x+3}+ \frac{3x+9}{(x-3)(2x+3)}=0x−32x+2x+31+(x−3)(2x+3)3x+9=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)}=0x−32x+2x+31+(x−3)(2x+3)3x+9=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(x−3)(2x+3)2x(2x+3)+(x−3)+3x+9=0
Cross multiply, we have,
2x(2x+3)+(x-3)+3x+9=(x-3)(2x+3)\times 02x(2x+3)+(x−3)+3x+9=(x−3)(2x+3)×0
simplify further, we have,
4x^2+6x+x-3+3x+9= 04x2+6x+x−3+3x+9=0
4x^2+10x+6= 04x2+10x+6=0
taking 2 common, we have,
2x^2+5x+3= 02x2+5x+3=0
Solving using middle term splitting method, we have,
5x can be written as 2x + 3x
2x^2+2x+3x+3= 02x2+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)= 02x(x+1)+3(x+1)=0
(2x+3)(x+1)= 0(2x+3)(x+1)=0
This implies, (x+1)= 0(x+1)=0 or (2x+3)= 0(2x+3)=0
This implies, x=-1x=−1 or x=\frac{-3}{2}x=2−3
Since, given x\neq \frac{-3}{2}x=2−3
thus, x = -1