Question

if no denominator is equal to zero, what is the solution set for the following equation?$\frac{4v-3}{v^2} = \frac{5}{2v}$select one:a. ${2}$b. ${-2}$c. ${-\frac{2}{5},2}$d. ${-\frac{2}{5},25}$question 22not yet answeredmarked out of 1.00flag questionif no denominator is equal to zero, what is the solution set for the following equation?$\frac{2k-5}{3k} - \frac{k+2}{4k} = \frac{k+6}{k}$select one:a. $k = -14$b. $k = -\frac{12}{7}$c. $k = -\frac{5}{12}$d. $k = -\frac{86}{7}$

Explanation:

First Equation: $\frac{4v-3}{v^2} = \frac{5}{2v}$

Step1: Eliminate denominators

Multiply both sides by $2v^2$ (the least common denominator, $v
eq 0$):
$$2v(4v-3) = 5v^2$$

Step2: Expand left side

$$8v^2 - 6v = 5v^2$$

Step3: Rearrange to standard quadratic form

Subtract $5v^2$ from both sides:
$$3v^2 - 6v = 0$$

Step4: Factor and solve

Factor out $3v$:
$$3v(v - 2) = 0$$
Solutions: $v=0$ (discarded, as it makes denominators zero) or $v=2$.

Step1: Eliminate denominators

Multiply all terms by $12k$ (the least common denominator, $k
eq 0$):
$$4(2k-5) - 3(k+2) = 12(k+6)$$

Step2: Expand all terms

$$8k - 20 - 3k - 6 = 12k + 72$$

Step3: Simplify left side

Combine like terms:
$$5k - 26 = 12k + 72$$

Step4: Isolate variable terms

Subtract $5k$ from both sides:
$$-26 = 7k + 72$$

Step5: Isolate constant terms

Subtract 72 from both sides:
$$-98 = 7k$$

Step6: Solve for $k$

Divide both sides by 7:
$$k = -14$$

Answer:

a. $\{2\}$

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Second Equation: $\frac{2k-5}{3k} - \frac{k+2}{4k} = \frac{k+6}{k}$