Question

I need help with number 90

Answer 1

Subtraction of the polynomial fractions $\frac{7t^{2} -t -4 }{t^{2} -25} -\frac{6t^{2}+12t -44}{t^{2} -25}$  is  $\frac{(t-8)}{(t+5)}$

How are the polynomial fractions subtracted?

Since the denominators of the fractions are same,

$\frac{({7t^{2} -t -4 }) -({6t^{2}+12t -44})}{t^{2} -25} \\\\=\frac{7t^{2} -t -4-6t^{2}-12t +44}{t^{2} -25} \\\\=\frac{t^{2} -13t +40 }{t^{2} -25}$

By, factorization of the polynomial fractions,

$\frac{t^{2} -13t +40 }{t^{2} -25}\\\\=\frac{(t-5)(t-8)}{(t+5)(t-5)}\\\\=\frac{(t-8)}{(t+5)}$

What are polynomial fractions?

• Polynomial fraction is the result of dividing one polynomial by another.

• By factorizing and reducing them to the lowest terms, a polynomial fraction can be made simpler when a polynomial appears in either the numerator or the denominator.

• A fraction in which either the numerator or the denominator are polynomials is the same as a rational expression.

• Factoring the polynomial entirely within the numerator and the denominator  is necessary in order to factor it completely.

To learn more about polynomial fractions, refer:

brainly.com/question/21191537

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