2
To solve this problem, we need to manipulate the given equation to find the value of the expression:
Given:
\(\frac{1}{x} = \frac{1}{p} + \frac{1}{q}\)
First, find a common denominator on the right-hand side:
\(\frac{1}{x} = \frac{q + p}{pq}\)
This implies:
\(x = \frac{pq}{p + q}\)
Substitute \(x\) in the given expression:
\(\frac{pq}{p^2-q^2}\left(\frac{x+p}{x-p}-\frac{x+q}{x-q}\right)\)
This equals:
\(\frac{pq}{p^2-q^2}\left(\frac{\left(\frac{pq}{p+q}\right)+p}{\left(\frac{pq}{p+q}\right)-p}-\frac{\left(\frac{pq}{p+q}\right)+q}{\left(\frac{pq}{p+q}\right)-q}\right)\)
First handle the two fractions separately:
- Let's simplify the first part:
\(\frac{\left(\frac{pq}{p+q}\right)+p}{\left(\frac{pq}{p+q}\right)-p} = \frac{\frac{pq + p(p + q)}{p+q}}{\frac{pq - p(p+q)}{p+q}}\) - Now simplify the second part:
\(\frac{\left(\frac{pq}{p+q}\right)+q}{\left(\frac{pq}{p+q}\right)-q} = \frac{\frac{pq + q(p + q)}{p+q}}{\frac{pq - q(p+q)}{p+q}}\)
Subtract these simplified terms:
\(-\frac{2pq + p^2}{p^2} + \frac{2pq + q^2}{q^2} = -1 +1\)
Finally, plug these back into the main expression:
\(\frac{pq}{p^2-q^2}\times 2 = 2\)
The correct answer is:
Option 2
Similar Questions
Let \(k\) be a positive integer. What is the quotient when \(x^{8k+3}+x^{8k+6}+x^{8k+9} + x^{8k+12}\) is divided by \((1+x^3)(1+x^6)\) ?
If 2s = a + b + c, then what is s(s-a)(s-b)(s-c) [ (1 / s-a) + (1 / s-b) + (1 / s-c) - (1 / s)] equal to?
- If \((x + 1)(x + p)(x^2 + p^2) = x^4 - 1\), then what is the value of \(p\)?
- If \((2+\sqrt{3})^x + (2-\sqrt{3})^x = 2\), then what is \((2+\sqrt{3})^x-(2-\sqrt{3})^x\) equal to?
What is
\(\frac{(a+b)^2}{(c-a)(c+a+b)} + \frac{(a+b)c}{c^2 + bc-a^2 - ab}\) - \(\frac{(a+2b + c)}{2(c-a)}\), \(a \neq b\), \(b \neq c\), \(c \neq a\)
equal to?
Which of the following is/are the factor(s) of \((3x + y)^2 + (3x+y)(x+5y)-20(x+5y)^2\)?
I. \((4x+13y)\)
II. \((x + 19y)\)
Select the correct answer using the code given below.
What is
\(\frac{\frac{x}{x-y}+\frac{y}{y-z}+\frac{z}{z-x}} {\frac{x+y}{x-y}+\frac{y+z}{y-z}+\frac{z+x}{z-x}+3}\)equal to?
- What is the value of p ?
What is the minimum value of p for which 1/532900 + p²/266450 + p⁴/523900 is an integer?
- If $p = \sqrt[3]{a + \sqrt{a^2 + b^3}} + \sqrt[3]{a - \sqrt{a^2 + b^3}}$, then what is $p^3 + 3bp$ equal to ?
Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
