Answer :
Let's carefully analyze each of the equations to determine which one is true.
### Option A:
[tex]\[ \frac{5}{8} = -\left(\frac{-5}{-8}\right) \][/tex]
First, simplify the right side:
[tex]\[ \frac{-5}{-8} = \frac{5}{8} \][/tex]
Therefore, the equation becomes:
[tex]\[ \frac{5}{8} = -\left(\frac{5}{8}\right) \][/tex]
This simplifies to:
[tex]\[ \frac{5}{8} = -\frac{5}{8} \][/tex]
Clearly, this is false since a positive number is not equal to its negative.
### Option B:
[tex]\[ \frac{-3}{-4} = -\frac{3}{4} \][/tex]
First, simplify the left side:
[tex]\[ \frac{-3}{-4} = \frac{3}{4} \][/tex]
Therefore, the equation becomes:
[tex]\[ \frac{3}{4} = -\frac{3}{4} \][/tex]
This simplifies to:
[tex]\[ \frac{3}{4} = -\frac{3}{4} \][/tex]
Again, this is false since a positive number is not equal to its negative.
### Option C:
[tex]\[ -\left(\frac{12}{-17}\right) = \frac{12}{17} \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ \frac{12}{-17} = -\frac{12}{17} \][/tex]
So the equation becomes:
[tex]\[ -\left(-\frac{12}{17}\right) = \frac{12}{17} \][/tex]
Simplify further:
[tex]\[ \frac{12}{17} = \frac{12}{17} \][/tex]
This equation is true since both sides are equal.
### Option D:
[tex]\[ \frac{9}{-13} = -\left(\frac{-9}{13}\right) \][/tex]
First, simplify the right side:
[tex]\[ \frac{-9}{13} = -\frac{9}{13} \][/tex]
So the equation becomes:
[tex]\[ \frac{9}{-13} = \frac{9}{13} \][/tex]
This simplifies to:
[tex]\[ -\frac{9}{13} = \frac{9}{13} \][/tex]
This is false since a negative number is not equal to its positive counterpart.
After evaluating each equation, we find that the true statement is:
[tex]\[ -\left(\frac{12}{-17}\right) = \frac{12}{17} \][/tex]
Thus the correct answer is C.
### Option A:
[tex]\[ \frac{5}{8} = -\left(\frac{-5}{-8}\right) \][/tex]
First, simplify the right side:
[tex]\[ \frac{-5}{-8} = \frac{5}{8} \][/tex]
Therefore, the equation becomes:
[tex]\[ \frac{5}{8} = -\left(\frac{5}{8}\right) \][/tex]
This simplifies to:
[tex]\[ \frac{5}{8} = -\frac{5}{8} \][/tex]
Clearly, this is false since a positive number is not equal to its negative.
### Option B:
[tex]\[ \frac{-3}{-4} = -\frac{3}{4} \][/tex]
First, simplify the left side:
[tex]\[ \frac{-3}{-4} = \frac{3}{4} \][/tex]
Therefore, the equation becomes:
[tex]\[ \frac{3}{4} = -\frac{3}{4} \][/tex]
This simplifies to:
[tex]\[ \frac{3}{4} = -\frac{3}{4} \][/tex]
Again, this is false since a positive number is not equal to its negative.
### Option C:
[tex]\[ -\left(\frac{12}{-17}\right) = \frac{12}{17} \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ \frac{12}{-17} = -\frac{12}{17} \][/tex]
So the equation becomes:
[tex]\[ -\left(-\frac{12}{17}\right) = \frac{12}{17} \][/tex]
Simplify further:
[tex]\[ \frac{12}{17} = \frac{12}{17} \][/tex]
This equation is true since both sides are equal.
### Option D:
[tex]\[ \frac{9}{-13} = -\left(\frac{-9}{13}\right) \][/tex]
First, simplify the right side:
[tex]\[ \frac{-9}{13} = -\frac{9}{13} \][/tex]
So the equation becomes:
[tex]\[ \frac{9}{-13} = \frac{9}{13} \][/tex]
This simplifies to:
[tex]\[ -\frac{9}{13} = \frac{9}{13} \][/tex]
This is false since a negative number is not equal to its positive counterpart.
After evaluating each equation, we find that the true statement is:
[tex]\[ -\left(\frac{12}{-17}\right) = \frac{12}{17} \][/tex]
Thus the correct answer is C.
