Advertisements
Advertisements
Question
Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
Advertisements
Solution
`1/"p" + 1/("q" + "r") = ("q" + "r" + "p")/("p"("q" + "r"))`
= `("p" + "q" + "r")/("p"("q" + "r"))`
`1/"p" - 1/("q" + "r") = ("q" + "r" - "p")/("p"("q" + "r"))`
`1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr") = (2"qr" + "q"^2 + "r"^2 - "p"^2)/(2"qr")`
= `(("q" + "r")^2 - "p"^2)/(2"qr")`
= `(("q" + "r" + "p")("q" + "r" - "p"))/(2"qr")`
= `(("p" + "q" + "r")("q" + "r" - "p"))/(2"qr")`
`(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
= `(("p" + "q" + "r"))/("p"("q" + "r")) xx ("p"("q" + "r"))/(("q" + "r" - "p")) xx (("p" + "q" + "r")("q" + "r" - "p"))/(2"qr")`
= `("p" + "q" + "r")^2/(2"qr")`
APPEARS IN
RELATED QUESTIONS
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
Simplify `("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
Subtract `1/(x^2 + 2)` from `(2x^3 + x^2 + 3)/(x^2 + 2)^2`
If A = `(2x + 1)/(2x - 1)`, B = `(2x - 1)/(2x + 1)` find `1/("A" - "B") - (2"B")/("A"^2 - "B"^2)`
If A = `x/(x + 1)` B = `1/(x + 1)` prove that `(("A" + "B")^2 + ("A" - "B")^2)/("A" + "B") = (2(x^2 + 1))/(x(x + 1)^2`
Pari needs 4 hours to complete the work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
Reduce the given Rational expression to its lowest form
`(10x^3 - 25x^2 + 4x - 10)/(-4 - 10x^2)`
At t minutes past 2 pm, the time needed to 3 pm is 3 minutes less than `("t"^2)/4`. Find t.
