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Problem 16

# Evaluate $$p=\\{(a-b)(a b+c)\\} /(c b-2 a)$$ When $$a=+2, b=-1 / 2$$, and $$c=-3$$

Expert verified
The expression $$p = \frac{(a-b)(ab+c)}{cb-2a}$$ evaluates to $$p=-2$$ when $$a=+2, b=-\frac{1}{2}$$, and $$c=-3$$.
See the step by step solution

## Step 1: Write down the given expression and variable values

The expression we are given is: $$p = \frac{(a-b)(ab+c)}{cb-2a}$$ And the given values are: $$a = +2$$, $$b = -\frac{1}{2}$$, and $$c = -3$$

## Step 2: Substitute the given values in the expression

Now, let's substitute the given values of a, b, and c into the expression for p: $$p = \frac{((2)-(-\frac{1}{2}))((2)(-\frac{1}{2})-(-3))}{(-3)(-\frac{1}{2})-2(2)}$$

## Step 3: Simplify the expression

Let's simplify the expression step-by-step: 1. Simplify inside the parentheses first: $$p = \frac{(2 + \frac{1}{2})(2*(-\frac{1}{2})+3)}{-3*(-\frac{1}{2})-(2*2)}$$ 2. Simplify the multiplication and addition within parentheses: $$p = \frac{(\frac{5}{2})(-1+3)}{\frac{3}{2}-4}$$ 3. Continue simplifying within parentheses: $$p = \frac{(\frac{5}{2})(2)}{-\frac{5}{2}}$$ 4. Simplify the fractions by cancelling out any common terms: $$p = \frac{(5)(2)}{(-5)}$$

## Step 4: Compute the final value of p

Now, compute the final value of the expression: $$p = -2$$ So, when $$a = +2$$, $$b = -\frac{1}{2}$$, and $$c = -3$$, the expression evaluates to: $$p = -2$$

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