Question

W2 \ w−9−18w−81 \ w−9

Answer 1

$\frac{w^2}{w-9} - \frac{18w-81}{w-9} = \frac{w^2-18+81}{w-9} = \frac{(w-9)^2}{w-9} = w-9$

Answer 2

To simplify the given expression, we need to combine like terms and factor out common factors. Let's break down the expression step by step:

Expression: (W^2 - 9) / (W - 9) - (18W - 81) / (W - 9)

Step 1: Factor the numerator of the first fraction (W^2 - 9) using the difference of squares formula.

W^2 - 9 = (W + 3)(W - 3)

Step 2: Factor out common factor (W - 9) from the numerator and denominator of both fractions.

(W + 3)(W - 3) / (W - 9) - [(18W - 81) / (W - 9)]

Step 3: Factor out 9 from the second fraction's numerator (18W - 81).

18W - 81 = 9(2W - 9)

Step 4: Replace the second fraction with the factored form.

(W + 3)(W - 3) / (W - 9) - [9(2W - 9) / (W - 9)]

Step 5: Now, we have a common denominator (W - 9) for both fractions. Combine the fractions.

[(W + 3)(W - 3) - 9(2W - 9)] / (W - 9)

Step 6: Expand the numerator by multiplying.

[W^2 - 3W + 3W - 9 - 18W + 81] / (W - 9)

Step 7: Simplify the numerator.

(W^2 - 18W + 81) / (W - 9)

Step 8: Factor the numerator, which is a quadratic expression.

W^2 - 18W + 81 = (W - 9)(W - 9)

Step 9: Cancel out the common factor in the numerator and denominator.

(W - 9)(W - 9) / (W - 9)

Step 10: The (W - 9) term in the numerator and denominator cancels out, leaving us with the final simplified expression:

W - 9

So, the simplified form of the given expression is (W - 9).