# How do you divide #(5x^2 + 22x + 8)/( 6x+8)#?

With this one, I fear you are into fractions!

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To divide (5x^2 + 22x + 8) by (6x + 8), you can use long division or synthetic division. Here is the solution using long division:

Step 1: Divide the first term of the numerator (5x^2) by the first term of the denominator (6x). The result is (5/6)x.

Step 2: Multiply the entire denominator (6x + 8) by the result from step 1, which is (5/6)x. This gives you (5/6)x * (6x + 8) = (5/6)x * 6x + (5/6)x * 8 = (5/6)x^2 + (20/3)x.

Step 3: Subtract the result from step 2 from the numerator (5x^2 + 22x + 8). This gives you (5x^2 + 22x + 8) - ((5/6)x^2 + (20/3)x) = (5x^2 + 22x + 8) - (5/6)x^2 - (20/3)x.

Step 4: Simplify the expression obtained in step 3. Combine like terms to get (5x^2 - (5/6)x^2) + (22x - (20/3)x) + 8 = (25/6)x^2 + (46/3)x + 8.

Step 5: Repeat steps 1-4 with the simplified expression from step 4. Divide the first term of the simplified numerator ((25/6)x^2) by the first term of the denominator (6x). The result is (25/36)x.

Step 6: Multiply the entire denominator (6x + 8) by the result from step 5, which is (25/36)x. This gives you (25/36)x * (6x + 8) = (25/36)x * 6x + (25/36)x * 8 = (25/36)x^2 + (100/9)x.

Step 7: Subtract the result from step 6 from the simplified numerator ((25/6)x^2 + (46/3)x + 8). This gives you (25/6)x^2 + (46/3)x + 8 - ((25/36)x^2 + (100/9)x) = (25/6)x^2 + (46/3)x + 8 - (25/36)x^2 - (100/9)x.

Step 8: Simplify the expression obtained in step 7. Combine like terms to get (25/6)x^2 - (25/36)x^2 + (46/3)x - (100/9)x + 8 = (25/6 - 25/36)x^2 + (46/3 - 100/9)x + 8 = (25/36)x^2 + (38/9)x + 8.

Therefore, the division of (5x^2 + 22x + 8) by (6x + 8) is equal to (25/36)x^2 + (38/9)x + 8.

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