Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.

If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 **-->**2y =30 -4y --> 6y =30 --> y=5. We could also work from the answers and substitute each answer in and solve.

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. However, because this problem has a minus sign, it first needs to be distributed. That would look as follows:

Taking a look at the given expression, we can see that we have two fractions divided by one another. The first fraction in the numerator is , and the second fraction in the denominator is .

Remember that when we have a fraction divided by a fraction, that is the same thing as multiplying the numerator by the reciprocal of the denominator. To simplify, we will do just that.

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To double check your answer, you can choose a numerical value for a and b and plug them into the expression.

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x + 4x2 – 8x + 16 = 2x3 + 16

5x – (6x – 2x) = 5x – (4x) = x

(x – 1)(x + 2) - x2 + 2 = x2 + x – 2 – x2 + 2 = x

x(4x)/(4x) = x

(3 – 3)x = 0x = 0

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.

x3 - 4x2 -12 + 15

You can then add -12 and 15, which equals 3.

You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.

In order to solve this problem, we need to look at each function separately and then derive expressions for f(a + b), f(a), and f(b). Then, we need to see whether f(a + b) = f(a) + f(b).

Let's start with the function 2_x_.

f(a + b) = 2(a+b)

Using our property of exponents that xyxz = x y+z, we can rewrite 2_a_+b.

f(a + b) = 2(a+b) = 2_a_2_b_

Now, let's derive an expression for f(a) + f(b).

f(a) = 2_a_, and f(b) = 2_b_. Thus, f(a) + f(b) = 2_a_ + 2_b_

Let's compare f(a + b) and f(a) + f(b).

Does 2_a_2_b_ = 2_a_ + 2_b_? It might, but not for every value of a and b. For example, let a and b both equal 0.

2020 = 1(1) = 1

20 + 20 = 1 + 1 = 2

If a and b are both zero, then it isn't true that f(a + b) = f(a) + f(b). Thus, f(x) = 2_x_ isn't special.

Next, let's examine the function f(x) = |x|.

f(a + b) = |a + b|

f(a) + f(b) = |a| + |b|

|a + b| doesn't always equal |a| + |b|. For example, if a = –1 and b = 1, then |a + b| = |–1 + 1| = 0, while f(a) + f(b) = |–1| + |1| = 1 + 1 = 2. Because f(a + b) is not always going to equal f(a) + f(b), the function f(x) = |x| isn't special.

The next function we can analyze is f(x) = _x_2.

f(a + b) = (a + b)2 = a_2 +2_ab + _b_2

f(a) + f(b) = _a_2 + _b_2

a_2 + 2_ab + _b_2 doesn't always equal _a_2 + _b_2 . Thus, f(x) = _x_2 isn't special.

The next function is f(x) = (x + 1)2 – _x_2. We can simplify f(x) a little bit to make it easier to work with.

f(x) = (x + 1)2 – _x_2 = (x_2 + 2_x + 1) – x_2 = 2_x + 1.

f(x) = 2_x_ + 1.

f(a + b) = 2(a + b) + 1 = 2_a_ + 2_b_ + 1

f(a) + f(b) = (2_a_ + 1) + (2_b_ + 1) = 2_a_ + 2_b_ + 2

2_a_ + 2_b_ + 1 doesn't equal 2_a_ + 2_b_ + 2, so this isn't a special function either.

This means that f(x) = (x + 1)2 – (x – 1)2 must be special. Let's see why.

First, let's simplify f(x).

f(x) = (x + 1)2 – (x – 1)2 = (x_2 + 2_x + 1) – (x_2 – 2_x + 1) = x_2 + 2_x + 1 – x_2 + 2_x – 1 = 4_x_.

f(x) = 4_x_.

f(a + b) = 4(a + b) = 4_a_ + 4_b_

f(a) + f(b) = 4_a_ + 4_b_

4_a_ + 4_b_ is always equal to 4_a_ + 4_b_. This means that the function is special.

The answer is f(x) = (x + 1)2 – (x – 1)2 .

Cross multiply to get 14ay = 15bx, then divide by 15b to get x by itself.

First, let's expand (a – b)2 using the FOIL method.

(a – b)(a – b) = _a_2 – ab – ba + _b_2 = a_2 – 2_ab + _b_2

The value of _a_2 + b_2 is already given to us. We can manipulate the equation ab = –8 to determine the value of –2_ab. Multiply both sides of the equation by –2.

–2_ab_ = 16

We will now substitute the values of –2_ab_ and _a_2 + _b_2 to find the value of (a – b)2.

(a – b)(a – b) = a_2 – 2_ab + _b_2 = 16 + 20 = 36

The answer is 36.