Advertisements
Advertisements
Question
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Advertisements
Solution
`(x+1)/(x-1)+(x-2)/(x+2)=4-(2x+3)/(x-2)`
`=>((x+1)(x+2)+(x-1)(x-2))/((x-1)(x+2))=(4(x-2)-(2x+3))/(x-2)`
`=>((x^2+2x+x+2)+(x^2-2x-x+2))/(x^2+2x-x-2)=(4x-8-2x-3)/(x-2)`
`=>(x^2+3x+2+x^2-3x+2)/(x^2+x-2)=(2x-11)/(x-2)`
`=>(2x^2+4)/(x^2+x-2)=(2x-11)/(x-2)`
⇒(2x2+4)(x−2)=(2x−11)(x2+x−2)
⇒2x3−4x2+4x−8=2x3+2x2−4x−11x2−11x+22
⇒2x3−4x2+4x−8=2x3−9x2−15x+22
⇒2x3−2x3−4x2+9x2+4x+15x−8−22=0
⇒5x2+19x−30=0
⇒5x2+25x−6x−30=0
⇒5x(x+5)−6(x+5)=0
⇒(5x−6)(x+5)=0
⇒5x−6=0, x+5=0
⇒x=`6/5`, x=−5
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations
(i) 7x2 = 8 – 10x
(ii) 3(x2 – 4) = 5x
(iii) x(x + 1) + (x + 2) (x + 3) = 42
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
Solve the Following Equation : x2- x - a (a + 1) = o
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
