solve the following for x: 3(3x-1/2x+3)-2(2x+3/3x-1)=5
Answers
you will get a simple quadratic equation
solve it
compare it to the assumes value
full solution is in picture
Given,
An expression: 3{(3x-1)/(2x+3)}-2{(2x+3)/(3x-1)}=5
To find,
The value of x.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that,
{(3x-1)/(2x+3)} = y ----------- {Equation-1}
By simplifying the given expression, we get;
3{(3x-1)/(2x+3)}-2{(2x+3)/(3x-1)}=5
=> 3{(3x-1)/(2x+3)}-2[1/{(3x-1)/(2x+3)}]=5
=> 3y - 2/y = 5
{according to equation-1}
=> (3y^2 - 2)/y = 5
=> 3y^2 - 2 = 5y
=> 3y^2 - 5y - 2 = 0
=> 3y^2 - 6y + y - 2 = 0
=> 3y(y-2) + 1(y-2) = 0
=> (y-2)(3y+1) = 0
=> (y-2) = 0 or (3y+1) = 0
=> y = 2 or y = (-1/3)
If y = 2
=> {(3x-1)/(2x+3)} = 2
{according to equation-1}
=> 3x-1 = 2(2x+3)
=> 3x - 1 = 4x + 6
=> x = -7
If y = (-1/3)
=> {(3x-1)/(2x+3)} = (-1/3)
{according to equation-1}
=> 3(3x-1) = (-1)(2x+3)
=> 9x - 3 = -2x - 3
=> 11x = 0
=> x = 0
Hence, the value of x is (-7) and 0.