Advertisements
Advertisements
Question
Simplify `("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
Advertisements
Solution
b2 + 3b – 28 = (b + 7) (b – 4)
b2 + 4b + 4 = (b + 2) (b + 2)
b2 – 49 = b2 – 72
= (b + 7) (b – 7)
b2 – 5b – 14 = (b – 7) (b + 2)
`("b"^2 + 3"b" - 28)/("b"^2 + 4"b" + 4) ÷ ("b"^2 - 49)/("b"^2 - 5"b" - 14)`
= `(("b" + 7)("b" - 4))/(("b" + 2)("b" + 2)) ÷ (("b" + 7)("b" - 7))/(("b" - 7)("b" + 2))`
= `(("b" + 7)("b" - 4))/(("b" + 2)("b" + 2)) xx (("b" + 2))/(("b" + 7))`
= `(("b" - 4))/(("b" + 2))`
APPEARS IN
RELATED QUESTIONS
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
`(x^3 - 27)/(x^3 + x^2 - 6x)`
Simplify `(x + 4)/(3x + 4y) xx (9x^2 - 16y^2)/(2x^2 + 3x - 20)`
Simplify `(x(x + 1))/(x - 2) + (x(1 - x))/(x - 2)`
Simplify `(x + 2)/(x + 3) + (x - 1)/(x - 2)`
Simplify `(x^3)/(x - y) + (y^3)/(y - x)`
Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ₹ 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?
Reduce the given Rational expression to its lowest form
`(x^(3"a") - 8)/(x^(2"a") + 2x^"a" + 4)`
Simplify `(1/("p") + 1/("q" + "r"))/(1/"p" - 1/("q" + "r")) xx [1 + ("q"^2 + "r"^2 - "p"^2)/(2"qr")]`
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
