If u = -3 and v = -\frac{1}{2}, what is the value of the algebraic expression below? Enter… — ACT

If $u = -3$ and $v = -\frac{1}{2}$ , what is the value of the algebraic expression below? Enter your numerical answer in the blank.

Answer:The value of the expression

\frac{4uv^2 - u^2}{2v - u}

is 【-6】.

The value of the expression when evaluated at

u = -3

and

v = -\frac{1}{2}

-6

Substituting

u = -3

and

v = -\frac{1}{2}

into the numerator gives

4(-3)(-\frac{1}{2})^2 - (-3)^2 = -3 - 9 = -12

. Substituting into the denominator gives

2(-\frac{1}{2}) - (-3) = -1 + 3 = 2

. Dividing

-12

2

results in

-6

Evaluate the terms containing exponents in the numerator.

v^2 = \left(-\frac{1}{2}\right)^2 = \frac{1}{4}

and

u^2 = (-3)^2 = 9

Exponents must be calculated before multiplication according to the order of operations.

Evaluate the numerator

4uv^2 - u^2

4(-3)\left(\frac{1}{4}\right) - 9 = -3 - 9 = -12

Multiply

4 \times (-3) \times \frac{1}{4}

to get

-3

, then subtract

9

Evaluate the denominator

2v - u

2\left(-\frac{1}{2}\right) - (-3) = -1 + 3 = 2

Multiplying

2

-\frac{1}{2}

gives

-1

, and subtracting negative

3

is equivalent to adding

3

Divide the numerator by the denominator.

\frac{-12}{2} = -6

Dividing

-12

2

yields the final result

-6

Evaluating algebraic expressions involving negative numbers, fractions, and order of operations.

Estimated Time:1m 30s

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