Advertisements
Advertisements
प्रश्न
Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Reduce the following rational expression to its lowest form
`(x^2 - 1)/(x^2 + x)`
Find the excluded values, of the following expression
`(x^2 + 6x + 8)/(x^2 + x - 2)`
Simplify `("p"^2 - 10"p" + 21)/("p" - 7) xx ("p"^2 + "p" - 12)/("p" - 3)^2`
Simplify `(x^3 - y^3)/(3x^2 + 9xy + 6y^2) xx (x^2 + 2xy + y^2)/(x^2 - y^2)`
Simplify `(x + 2)/(4"y") ÷ (x^2 - x - 6)/(12y^2)`
If x = `("a"^2 + 3"a" - 4)/(3"a"^2 - 3)` and y = `("a"^2 + 2"a" - 8)/(2"a"^2 - 2"a" - 4)` find the value of x2y–2
Subtract `1/(x^2 + 2)` from `(2x^3 + x^2 + 3)/(x^2 + 2)^2`
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 4)`
`(3y - 3)/y ÷ (7y - 7)/(3y^2)` is
Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
