Question Simplify the expression $3-\frac{3}{10 y^{2}}$ and express the answer as a single fraction in simplest form.

Studdy Solution

STEP 1

1. The expression $3-\frac{3}{10y^2}$ involves real numbers and the variable $y$ .
2. The expression can be simplified by finding a common denominator and combining terms.
3. The final expression should be a single fraction in simplest form.

STEP 2

1. Identify the least common denominator (LCD) for the two terms.
2. Rewrite each term with the LCD as the denominator.
3. Combine the terms over the common denominator.
4. Simplify the resulting fraction if possible.

STEP 3

Identify the least common denominator (LCD) for the two terms $3$ and $\frac{3}{10y^2}$ .
The LCD for the given terms is $10y^2$ since the second term already has $10y^2$ in the denominator and the first term is an integer which can be expressed with any denominator.

STEP 4

Rewrite the first term $3$ with the LCD $10y^2$ as the denominator.
$3 = \frac{3}{1} = \frac{3 \cdot 10y^2}{10y^2} = \frac{30y^2}{10y^2}$

STEP 5

Rewrite the second term $\frac{3}{10y^2}$ with the LCD $10y^2$ as the denominator.
$\frac{3}{10y^2} = \frac{3}{10y^2}$ (No change is needed since the term already has the LCD as its denominator.)

STEP 6

Combine the terms over the common denominator $10y^2$ .
$3 - \frac{3}{10y^2} = \frac{30y^2}{10y^2} - \frac{3}{10y^2} = \frac{30y^2 - 3}{10y^2}$

STEP 7

Simplify the resulting fraction if possible.
$\frac{30y^2 - 3}{10y^2} = \frac{3(10y^2 - 1)}{10y^2}$ Since there are no common factors between the numerator and the denominator that can be cancelled, the fraction is already in its simplest form.
The simplified expression in simplest form is: $\frac{3(10y^2 - 1)}{10y^2}$

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