Question

Solve the equation - 2(3x+5/x+2) -5(x+2/3x-5) = 3 , where x unequal -2 and x unequal 5/3

it's urgent
please quys
with solution

Answer 1

Explanation:

(a - b)(a + b) =a² - b²

(3x + 5)(3x -5) =(3x)² - 5² = 9x² - 25

(x +2)(x+2) = (x+ 2)² = x²+ 2*2*x+2² = x² + 4x + 4

(x+2)(3x -5 ) = x*3x - 5*x +2*3x +2*(-5)

= 3x² -5x +6x -10

= 3x² + x - 10

`(2*(3x+5))/(x+2)-(5(x+2))/(3x-5)=3\\\\(2*(3x+5)*(3x-5))/((x+2)(3x-5))-(5*(x+2)(x+2))/((3x-5)(x+2))=3\\\\(2*(9x^(2)-25)-5(x^(2)+4x+4))/((3x-5)(x+2))=3`

`(18x^(2)-25-5x^(2)-20x-20)/(3x^(2)+x-10)=3\\\\(18x^(2)-5x^(2)-20x - 25-20)/(3x^(2)+x-10)=3\\\\`

13x² - 20x - 45 = 3*(3x² + x - 10)

13x² - 20x - 45 =9x² + 3x - 30

13x² - 9x² -20x - 3x - 45 + 30 = 0

4x² - 23x - 15 = 0