25 points for grabs!

Mathematics

1 answer:

coldgirl [10]4 years ago

3 0

Answer:

6 marbles

Step-by-step explanation:

Let the initial number of marbles be x

Then added 3 and got 9 as final number

<u>Equation for this and solution</u>

x + 3 = 9
x = 9 - 3
x = 6

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notsponge [240]

Option 3

The solution for given expression is $\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}$

<h3><u>Solution:</u></h3>

Given that we have to divide,

$\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}$ ---- (A)

Let us first factorize each term and then solve the sum

Using $a^2 - b^2 = (a + b)(a - b)$

$x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)$ ----- (1)

$x^2 + 5x + 6 = (x + 2)(x + 3)$ ----- (2)

$x^2 + 5x + 4 = (x+1)(x + 4)$ ---- (3)

$x^2 -2x - 8 = (x-4)(x + 2)$ ---- (4)

Now substituting (1), (2), (3), (4) in (A) we get,

$\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}$

To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.

$\frac{(x + 4)(x -4)}{(x +2)(x +3)} \times \frac{(x - 4)(x + 2)}{(x + 1)(x + 4)}$