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gregori [183]
1 year ago
8

PLEASE GUYS THIS IS THE HARDEST MATH PORBLEMS PLEASE ASAP PLEASE I NEED HELP PLEASE T_T

Mathematics
1 answer:
Alexandra [31]1 year ago
7 0

The simplified form of R(x) is R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}

<h3>Simplifying an expression </h3>

From the question, we are to simplify the expression

From the given information,

f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}

and

g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}

Also,

R(x) = f(x) \div g(x)

∴ R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}

R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}

Factoring each of the quadratics

R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}

R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}

R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}

Simplifying

R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}

R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}

R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}

R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}

Hence, the simplified form of R(x) is R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}

Learn more on Simplifying an expression here: brainly.com/question/1280754

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