# Tutor profile: Aparna N.

## Questions

### Subject: Basic Math

What is 1/2 + 1/3 = ?

If we want to solve this problem we have to make sure the denominators are the same. The denominators are the numbers on the bottom of a fraction. In this case, the denominator of 1/2 is 2 and the denominator of 1/3 is 3. How do we get the denominators to be the same? Well we can multiply the fractions by a whole number so that the denominators end up being the same. If we multiply 1/2 by 3 we get 3/6 If we multiply 1/3 by 2 we get 2/6 Wow! Now that the denominators are the same we can add them up 1 1 3 + 2 __ + ___ is the same as writing ____ ____ 2 3 6 6 So to add fractions we add the numerators (or top numbers) together in this case it is 3 + 2 which is 5 When adding fractions, the denominators will be the same So, the answer is 5/6

### Subject: Calculus

Find the derivative of the following equation: x^3 - 4x^2 + 17x - 9

When finding the derivative we have to remember a few rules: 1. We bring down the exponent in front of the constant 2. We multiply the constant by the exponent 3. Subtract one from the new exponent for x 4. If it is only a constant, the derivative will be 0 Using this we see that the derivative of the equation is 3x^2 - 8x +17

### Subject: Algebra

Simplify the following equation and solve for x: 6(- 3x - 4) - (x - 2) = -4x + 27

To begin simplifying we want to look at the equation from LEFT to RIGHT Step 1: Multiply the 6 out -> In this case, we will multiply the 6 into the first set of parenthesis -> so we will do (6*-3x - 6*4) This gives us -18x - 24 - (x-2) = -4x +27 Step 2: Multiply the negative sign out -> In this case, we will multiply the negative sign (-) into the second set of parenthesis -> so we will do (-x - -2) -> The two negatives make a positive so it becomes (-x +2) Plugging this into the overall equation gives -18x - 24 -x +2 = -4x +27 We are now ready to start combining like terms Step 5: Combine all the terms with X on the LEFT side -> If we combine the -18x and -x on the left side it will give us -19x So how do we combine the -19x with the -4x? Step 6: Get all the X terms on one side -> If we add 19x to both sides then the equation will look like -19x +19x -24+2 = -4x +19x +27 -> The terms on the LEFT side can be cancelled so the equation now looks like: -24 +2 = -4x +19x +27 Step 7: Combine all X terms -24+2 = 15x +27 Step 8: Combine the Non-X terms on the LEFT side -22 = 15x +27 Step 9: Get all the non-X terms on one side -> We will do this by subtracting 27 from both sides -> This gives the equation -22 - 27 = 15x + 27 -27 -> Since the right side cancels out we are left with -22 - 27 = 15x Step 10: Combine the right side terms -49 = 15x Step 11: Get X by itself -> We do this by dividing both sides by 15 This gives us -49/15 = x So our final answer is -49/15 or 3.2666

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