Math

QuestionMultiply: 3x37x+74x+414x14\frac{3 x-3}{7 x+7} \cdot \frac{4 x+4}{14 x-14}

Studdy Solution

STEP 1

Assumptions1. We are given two fractions to multiply. . The fractions are 3x37x+7\frac{3x-3}{7x+7} and 4x+414x14\frac{4x+4}{14x-14}.
3. We are assuming that xx is not equal to 1-1 or 00, as these values would make the denominators of the fractions equal to zero, which is undefined.

STEP 2

We start by simplifying each fraction if possible. We notice that in each fraction, both the numerator and denominator have common factors. We can factor out these common factors.
The first fraction becomesx7x+7=(x1)7(x+1)\frac{x-}{7x+7} = \frac{(x-1)}{7(x+1)}The second fraction becomes4x+414x14=4(x+1)14(x1)\frac{4x+4}{14x-14} = \frac{4(x+1)}{14(x-1)}

STEP 3

Now, we multiply the fractions together.3(x1)7(x+1)(x+1)14(x1)\frac{3(x-1)}{7(x+1)} \cdot \frac{(x+1)}{14(x-1)}

STEP 4

We notice that (x1)(x-1) in the numerator of the first fraction and (x1)(x-1) in the denominator of the second fraction cancel each other out. Similarly, (x+1)(x+1) in the denominator of the first fraction and (x+1)(x+1) in the numerator of the second fraction cancel each other out.
3(x1)7(x+1)4(x+1)14(x1)=37414\frac{3(x-1)}{7(x+1)} \cdot \frac{4(x+1)}{14(x-1)} = \frac{3}{7} \cdot \frac{4}{14}

STEP 5

Now, we simplify the remaining fractions37414=34714\frac{3}{7} \cdot \frac{4}{14} = \frac{3 \cdot4}{7 \cdot14}

STEP 6

We simplify the multiplication3414=1298\frac{3 \cdot4}{ \cdot14} = \frac{12}{98}

STEP 7

Finally, we simplify the fraction 1298\frac{12}{98} by dividing the numerator and the denominator by their greatest common divisor, which is21298=649\frac{12}{98} = \frac{6}{49}So, the solution to the problem is 649\frac{6}{49}.

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