Advertisements
Advertisements
प्रश्न
Simplify `(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
Advertisements
उत्तर
2a2 + 5a + 3a + 3 = 2a2 + 2a + 3a + 3
= 2a(a + 1) + 3 (a + 1)
= (a + 1) (2a + 3)
2a2 + 7a + 6 = 2a2 + 3a + 4a + 6
= a(2a + 3) + 2 (2a + 3)
= (2a + 3) (a + 2)
a2 + 6a + 5 = (a + 5) + (a + 1)
– 5a2 – 35a – 50 = – 5(a2 + 7a + 10)
= – 5(a + 5)(a + 2)
`(2"a"^2 + 5"a" + 3)/(2"a"^2 + 7"a" + 6) ÷ ("a"^2 + 6"a" + 5)/(-5"a"^2 - 35"a" - 50)`
= `(("a" + 1)(2"a" + 3))/((2"a" + 3)("a" + 2)) ÷ (("a" + 5)("a" + 1))/(-5("a" + 5)("a" + 2))`
= `(("a" + 1))/(("a" + 2)) ÷ (("a" + 1))/(-5("a" + 2))`
= `(("a" + 1))/(("a" + 2)) xx (-5("a" + 2))/(("a" + 1))`
= – 5
APPEARS IN
संबंधित प्रश्न
Reduce the following rational expression to its lowest form
`(9x^2 + 81x)/(x^3 + 8x^2 - 9x)`
Reduce the following rational expression to its lowest form
`("p"^2 - 3"p" - 40)/(2"p"^3 - 24"p"^2 + 64"p")`
Find the excluded values, of the following expression
`y/(y^2 - 25)`
Simplify `("p"^2 - 10"p" + 21)/("p" - 7) xx ("p"^2 + "p" - 12)/("p" - 3)^2`
Simplify `("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
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?
Arul, Madan and Ram working together can clean a store in 6 hours. Working alone, Madan takes twice as long to clean the store as Arul does. Ram needs three times as long as Arul does. How long would it take each if they are working alone?
Is it possible to design a rectangular park of perimeter 320 m and area 4800 m2? If so find its length and breadth.
Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.
`{:("April sale in" ₹)/("rice" "wheat" "ragi"):}`
A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`
and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.
What is the average sales for the months of April and May
Two farmers Thilagan and Kausigan cultivates three varieties of grains namely rice, wheat and ragi. If the sale (in ₹) of three varieties of grains by both the farmers in the month of April is given by the matrix.
`{:"April sale in" ₹)/("rice" "wheat" "ragi":}`
A = `[(500, 1000, 1500),(2500, 1500, 500)]"Thilagan"/"Kausigan"`
and the May month sale (in ₹) is exactly twice as that of the April month sale for each variety.
If the sales continue to increase in the same way in the successive months, what will be sales in the month of August?
