Solve the following quadratic equation by factorization. \frac{2x}{x-3}+\frac{1}{2x+3}+\frac{3x+9}{(x-3)(2x+3)}=0

PEEWSRIGWETRYqx

PEEWSRIGWETRYqx

Answered question

2021-12-18

Solve the following quadratic equation by factorization.
2xx3+12x+3+3x+9(x3)(2x+3)=0

Answer & Explanation

Elaine Verrett

Elaine Verrett

Beginner2021-12-19Added 41 answers

Given
2xx3+12x+3+3x+9(x3)(2x+3)=0
Step by step solution
2x(2x+3)+1(x3)+3x+4(x3)(2x+3)
4x2+6x+x3+3x+9=0
4x2+10x+6=0
2(2x2+5x+3)=0
2x2+5x+3=0
Complete Solution
2x2+5x+3=0
2x2+2x+3x+3=0
2x(x+1)+3(x+1)=0
(x+1)(2x+3)=0
x=1
or
2x+3=0
x=32
Paul Mitchell

Paul Mitchell

Beginner2021-12-20Added 40 answers

Step 1
Given equation is 2xx3+12x+3+3x+9(x3)(2x+3)=0
Upon simplification this can be written as:
2x(2x+3)+1(x3)+3x+9(x3)(2x+3)=0
Taking denominator to the right hand side
2x(2x+3)+1(x-3)+3x+9=0
Step 2
4x2+6x+x3+3x+9=0
4x2+10x+6=0
4x2+4x+6x+6=0
4x(x+1)+6(x+1)=0
(4x+6)(x+1)=0
4x+6=0 or x+1=0
4x=6 or x=-1
x=64 or x=-1
x=32 or x=-1
Therefore x=-1.5 or -1
nick1337

nick1337

Expert2021-12-28Added 777 answers

Step 1
Factorization method:-
2xx3+12x+3+3x+9(x3)(2x+3)=02x(2x+3)+(x3)+3x+9(x3)(2x+3)=04x2+6x+x3+3x+9=04x2+10x+6=04x2+4x+6x+6=04x(x+1)+6(x+1)=0(x+1)(4x+6)=0x+1=0 or 4x+6=0x=1,32
But x32
Step 2
Thus, x=-1 is the solution of the given equation

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