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
`(x^2 - 1)/(x^2 + x)`
Find the excluded values, of the following expression
`"t"/("t"^2 - 5"t" + 6)`
Simplify `(5"t"^3)/(4"t" - 8) xx (6"t" - 12)/(10"t")`
Simplify `(4x)/(x^2 - 1) - (x + 1)/(x - 1)`
Identify rational expression should be subtracted from `(x^2 + 6x + 8)/(x^3 + 8)` to get `3/(x^2 - 2x + 4)`
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`
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?
Solve `1/3` (x + y – 5) = y – z = 2x – 11 = 9 – (x + 2z)
One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections
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?
