Question

solve the quadratic equation. 1/2x-3+1/x-5=10/9. ,x is not equal to 3/2,5

Answer 1

I hope this may also will help you

Answer 2

Given,

1/(2x-3) + 1/(x-5) = 10/9

To find,

The value of x.

Solution,

The values of x after solving the given equation will be 6 and 37/20.

We can easily solve this problem by following the given steps.

According to the question,

1/(2x-3) + 1/(x-5) = 10/9

Taking the LCM of the denominators and adding the two fractions,

(x-5) + (2x-3)/(2x-3) (x-5) = 10/9

3x-8/(2x² -13x + 15) = 10/9 [ Using the identity (x+a)(x+b) = x² + (a+b)x + ab]

Using the cross multiplication method,

9(3x-8) = 10(2x²-13x+15)

27x - 72 = 20x² - 130x + 150 [ Multiplying the numbers into the brackets]

20x² - 130x + 150 = 27x-72

20x² - 130x - 27x + 150 + 72 = 0 ( Moving 27x and 72 from the right-hand side to the left-hand side results in the change of their sign from plus to minus and minus to plus.)

20x² - 157x + 222 = 0

Factorising this equation by splitting the middle term into two terms such that their multiplication will be 20x² × 222 and their addition will give -157x,

20x² - 120x - 37x + 222 = 0

20x (x-6) - 37(x-6) = 0 [ Taking 20x common from the first two terms and -37 from the last two terms]

(x-6) (20x-37) = 0

Equating the brackets to zero,

x-6 = 0, 20x-37 = 0

x = 6, x = 37/20

Hence, the values of x after solving the given equation are 6 and 37/20.