Question

$x \div x - 1 + x - 1 \div 3 = 5 \div 2$
solve it plz!! ​

Answer 1

Answer:

Step-by-step explanation:

Given that,

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

⇒ 3 × ( x ) + ( x - 1 )^2 / 3 ( x - 1 ) = 5 / 2

⇒ 3x + [ ( x )^2 + ( 1 )^2 - 2 × x × 1 ] / ( 3x - 3 ) = 5 / 2

⇒3x + x ^2 + 1 - 2x / ( 3x - 3 ) = 5 / 2

⇒ x^2 + x + 1 / ( 3x - 3 ) = 5 / 2

⇒ by cross multiplication, we get

⇒ 2 ( x^2 + x + 1 ) = 5 ( 3x - 3 )

⇒ 2x ^2 + 2x + 2 = 15x - 15

⇒2x ^2 + 2x + 2 - 15x + 15 = 0

⇒ 2x ^2 - 13x + 17 = 0

Now compare the above equation with standard quadratic equation ax^2 +bx +c,we get

a = 2 , b = - 13 , c = 17

So , x = -b ± √ (b)^2 - 4ac

= - ( - 13 ) ± √ ( - 13 )^2 - 4 × 2 × 17 / (2 × 2)

= 13 ± √ 169 - 136 / (4)

= 13 ± √ 33 / (4)

= 13 + √ 33 / 4 or 13 - √ 33 / 4

∴ x = 13 + √33 / 4 or 13 - √33 / 4 is the answer