Solved on Dec 10, 2023

Find the missing value in the equation: $\frac{\square}{t+7} \times \frac{3(t+7)}{t+1}=\frac{15(t+13)}{t+1}$

STEP 1

Assumptions
1. We are given a fraction equation with a missing numerator represented by a square.
2. We need to find the value of the missing expression to make the equation true for all values of $t$ where the equation is defined (i.e., $t \neq -7$ and $t \neq -1$ ).

STEP 2

First, we will simplify the left side of the equation by canceling out common factors.
$\frac{\square}{t+7} \times \frac{3(t+7)}{t+1} = \frac{\square \times 3}{t+1}$

STEP 3

Now, the equation looks like this:
$\frac{\square \times 3}{t+1} = \frac{15(t+13)}{t+1}$

STEP 4

Since the denominators on both sides of the equation are the same, we can equate the numerators directly.
$\square \times 3 = 15(t+13)$

STEP 5

Divide both sides of the equation by 3 to solve for the missing expression (represented by the square).
$\square = \frac{15(t+13)}{3}$

STEP 6

Simplify the right side of the equation by distributing the 15 and then dividing by 3.
$\square = 5(t+13)$

STEP 7

Further simplify the expression by distributing the 5.
$\square = 5t + 65$
The missing expression in the calculation is $5t + 65$ .

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Find the missing value in the equation: $\frac{\square}{t+7} \times \frac{3(t+7)}{t+1}=\frac{15(t+13)}{t+1}$

STEP 1

Assumptions
1. We are given a fraction equation with a missing numerator represented by a square.
2. We need to find the value of the missing expression to make the equation true for all values of $t$ where the equation is defined (i.e., $t \neq -7$ and $t \neq -1$ ).

STEP 2

First, we will simplify the left side of the equation by canceling out common factors.
$\frac{\square}{t+7} \times \frac{3(t+7)}{t+1} = \frac{\square \times 3}{t+1}$

STEP 3

Now, the equation looks like this:
$\frac{\square \times 3}{t+1} = \frac{15(t+13)}{t+1}$

STEP 4

Since the denominators on both sides of the equation are the same, we can equate the numerators directly.
$\square \times 3 = 15(t+13)$

STEP 5

Divide both sides of the equation by 3 to solve for the missing expression (represented by the square).
$\square = \frac{15(t+13)}{3}$

STEP 6

Simplify the right side of the equation by distributing the 15 and then dividing by 3.
$\square = 5(t+13)$

STEP 7

Further simplify the expression by distributing the 5.
$\square = 5t + 65$
The missing expression in the calculation is $5t + 65$ .

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Find the missing value in the equation: □t+7×3(t+7)t+1=15(t+13)t+1\frac{\square}{t+7} \times \frac{3(t+7)}{t+1}=\frac{15(t+13)}{t+1}t+7□​×t+13(t+7)​=t+115(t+13)​

STEP 1

STEP 2

First, we will simplify the left side of the equation by canceling out common factors.□t+7×3(t+7)t+1=□×3t+1 \frac{\square}{t+7} \times \frac{3(t+7)}{t+1} = \frac{\square \times 3}{t+1} t+7□​×t+13(t+7)​=t+1□×3​

STEP 3

Now, the equation looks like this:□×3t+1=15(t+13)t+1 \frac{\square \times 3}{t+1} = \frac{15(t+13)}{t+1} t+1□×3​=t+115(t+13)​

STEP 4

Since the denominators on both sides of the equation are the same, we can equate the numerators directly.□×3=15(t+13) \square \times 3 = 15(t+13) □×3=15(t+13)

STEP 5

Divide both sides of the equation by 3 to solve for the missing expression (represented by the square).□=15(t+13)3 \square = \frac{15(t+13)}{3} □=315(t+13)​

STEP 6

Simplify the right side of the equation by distributing the 15 and then dividing by 3.□=5(t+13) \square = 5(t+13) □=5(t+13)

STEP 7

Further simplify the expression by distributing the 5.□=5t+65 \square = 5t + 65 □=5t+65The missing expression in the calculation is 5t+65 5t + 65 5t+65.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the missing value in the equation: $\frac{\square}{t+7} \times \frac{3(t+7)}{t+1}=\frac{15(t+13)}{t+1}$

First, we will simplify the left side of the equation by canceling out common factors.
$\frac{\square}{t+7} \times \frac{3(t+7)}{t+1} = \frac{\square \times 3}{t+1}$

Now, the equation looks like this:
$\frac{\square \times 3}{t+1} = \frac{15(t+13)}{t+1}$

Since the denominators on both sides of the equation are the same, we can equate the numerators directly.
$\square \times 3 = 15(t+13)$

Divide both sides of the equation by 3 to solve for the missing expression (represented by the square).
$\square = \frac{15(t+13)}{3}$

Simplify the right side of the equation by distributing the 15 and then dividing by 3.
$\square = 5(t+13)$

Further simplify the expression by distributing the 5.
$\square = 5t + 65$
The missing expression in the calculation is $5t + 65$ .