Question

Simplify the expression. $$-\frac{3}{5}\left(-\frac{5}{3} x\right)$$

Short answer

The given expression simplifies to just \(x\).

Step-by-step solution

Analyze the given expression

The given expression is -\(\frac{3}{5}\left(-\frac{5}{3}x\right)\). This consists of the multiplication of three terms, a negative number, a fraction, and a variable x. Remember that multiplication is an associative operation, and thus the order in which the multiplications are executed won't affect the final result.

Multiply the fractions

Start by multiplying the fractions in the given expression. This is done by multiplying the numerators with each other and the denominators with each other. The multiplication of fractions leaves us with - \(\frac{3}{5} \times -\frac{5}{3} = - \frac{3 \times -5}{5 \times 3}\) which simplifies to - \(\frac{-15}{15}\).

Simplify the result from step 2

The result from Step 2 simplifies to -\(-1\) because division of the same numbers gives us 1 and the negative sign gets cancelled by the negative of the numerator.

Handling the variable 'x'

In the original expression, the variable 'x' was being multiplied by the bracketed term. After simplifying the bracketed expression in the previous steps, 'x' needs to be multiplied (-1). This gives us the final expression as \(1x \) or simply \(x\).