Question

solve the following quadratic equation 4/x-3 =5/2x+3 by factorization method​

Answer 1

Step-by-step explanation:

Answer:

The solution of the expression is x=-2 and x=1.

Step-by-step explanation:

Given : Expression (\frac{4}{x})-3=\frac{5}{2x+3}(

x

4

)−3=

2x+3

5

To find : Solve by factorization?

Solution :

Solve the expression,

(\frac{4}{x})-3=\frac{5}{2x+3}(

x

4

)−3=

2x+3

5

\frac{4-3x}{x}=\frac{5}{2x+3}

x

4−3x

=

2x+3

5

Cross multiply,

(4-3x)(2x+3)=5x(4−3x)(2x+3)=5x

8x+12-6x^2-9x=5x8x+12−6x

2

−9x=5x

6x^2+6x-12=06x

2

+6x−12=0

x^2+x-2=0x

2

+x−2=0

Apply middle term split,

x^2+2x-x-2=0x

2

+2x−x−2=0

x(x+2)-1(x+2)=0x(x+2)−1(x+2)=0

(x+2)(x-1)=0(x+2)(x−1)=0

x=-2,1x=−2,1

Therefore, The solution of the expression is x=-2 and x=1.