Problem

Find the quotient and simplify the result. \[ \frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16} \] $\frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16}=\square($ Simplify your answer.)

Solution

Step 1 :Given the division of two fractions: \(\frac{x+9}{2-x} \div \frac{x^{2}-14 x+48}{x^{2}-10 x+16}\)

Step 2 :We know that the division of two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.

Step 3 :So, we find the reciprocal of the second fraction: \(\frac{x^{2}-10 x+16}{x^{2}-14 x+48}\)

Step 4 :Then, we multiply the first fraction by the reciprocal of the second fraction: \(\frac{x+9}{2-x} \times \frac{x^{2}-10 x+16}{x^{2}-14 x+48}\)

Step 5 :This gives us: \(\frac{(x + 9)*(x^{2} - 10*x + 16)}{(2 - x)*(x^{2} - 14*x + 48)}\)

Step 6 :We can simplify this result by factoring the polynomials and cancelling out the common factors.

Step 7 :The simplified result of the division is \(\boxed{\frac{-x - 9}{x - 6}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/nwxLmZ0H8d/

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