Mathematics.?

Question

1a) Solve the equation 1 + 2/x = 3/2.

1b) Given that a = square root b + 2 / c,
express b in terms of a and c.

1c) Express the following as a single fraction, in its simplest form,

(i) K^2 - k / K^2 - 1.
(ii) 1 / x - 3 - 2 / 3 - x.

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Answer 1

1 + 2/x = 3/2

Multiply both sides of the equation by 2x

2x(1) + 2x(2/x) = 2x(3/2)

2x + 4 = 3x

Transpose 2x

2x + 4 - 2x = 3x - 2x

Collect like terms

4 = x

- - - - - - - -s-

Answer 2

>1a) Solve the equation 1 + 2/x = 3/2.
2/x = 3/2 - 1 = 1/2
Multiply across by x
2 = x/2
4 = x

>1b) Given that a = √b + 2 / c,
express b in terms of a and c.

Make b the subjest of the equation => isolate the b term on the RHS by subtracting 2/c from both sides
a = √b + 2 / c
a -2/c = √b
Square both sides
b = (a -2/c)²
= (ac-2)²/c² if you prefer

>1c) Express the following as a single fraction, in its simplest form

(i) K^2 - k / K^2 - 1
Are 'k' and 'K' supposed to be the same variable or different?
And there are no brackets on anything?
If they are the same:
k² - k/k² - 1 = k² - k/k² - 1
= k² - 1/k - 1
= (k³ - k -1)/k

>(ii) 1 / x - 3 - 2 / 3 - x
Again you wrote no brackets e.g around the "3 - x", so the answer to what you wrote is...
1/x - 3 - 2/3 - x = 1/x - 11/3 - x
= (1 - 11x/3 - x²)/x
= (3 - 11x - 3x²)/3x

(Take more care with your brackets...)

Answer 3

1a) 1=+2/x=2/3
multiply the equation by 2x:
2x+4=3x
substract 2x from both sides:
4= 3x -2x
therefore x = 4
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1b)a = square root b+2/c
by squaring both sides:
a^2 = b+2/c
substract 2/c from both sides:
a^2 - 2/c =b
therefore b = a^2 - 2/c
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1c)
(i)k^2 - k/k^2 - 1
by analysing:
k(k-1) / (k-1)(k+1)
= k/k+1
------------------------
(ii)1/x - 3 - 2/3 - x
by uniting the denomiator making it 3x:
3 - 9x - 2x - 3x^2 / 3x
= 3 - 11x - 3x^2/ 3x

hope i helped you......

Answer 4

1)
1 + 2/x = 3/2.
2/x = 3/2 - 1
2/x = 1/2
x = 4

2)
a = square root b + 2 / c,
a - 2/c = sqrt b
(a - 2/c)^2 = b
b = a^2 - 4a/c + 4/c^2

3)
(i) K^2 - k / K^2 - 1
= k(k-1)/(k-1)(k+1)
= k/(k+1)
.
(ii) 1 / x - 3 - 2 / 3 - x.
= (3-x)/[(x-3)(3-x)] - (2x-6)/[(3-x)(x-3)]
= (3 - x - 2x + 6)/[(3-x)(x-3)]
= (9-3x)/[(3-x)(x-3)]
= 3(3-x)/[(3-x)(x-3)]
= 3/(x-3)

Answer 5

1a.(x+2)/x=3/2
2x+4=3x
x=4


1b. a=sqroot(b+2/c)
a^2=b+2/c
a^2c=bc+2
(a^2c-2)/c=b


c.i

k(k-1)/(k-1)(k+1)
=k/(k+1)

c(ii)


on taking LCM
we get
(3-x-2x+6)/(-x^2+6x-9)
(-3x+9)/-(x-3)^2
3/(x-3)