Question

do asap please tomorrow is my exam

Answer 1

Hey there!

a) Inverse the numerator and the denominator for multiplying the products, to continue the simplification of the given expression:

$\bf{\dfrac{x^2 - 7x + 6}{x + 4} \times \dfrac{x^2 - 16}{(x - 1)^2}}$

$\bf{\dfrac{\Big(x^2 - 7x + 6 \Big) \Big(x^2 - 16 \Big)}{(x + 4)(x - 1)^2}}$

$\bf{\dfrac{(x - 1)(x - 6)(x^2 - 16)}{(x - 1)^2 (x + 4)}}$

$\bf{\dfrac{(x - 6)(x^2 - 16)}{(x + 4)(x - 1)}}$

$\bf{\dfrac{(x - 6)(x + 4)(x - 4)}{(x + 4)(x - 1)}}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: \: \dfrac{(x - 6)(x - 4)}{x - 1}}}}$

b) Cancel out the common factors, to get the solution:

$\bf{6pq - \dfrac{12pq^2}{6pq}}$

$\bf{6pq - \dfrac{2pq^2}{pq}}$

$\bf{6pq - \dfrac{2q^2}{q}}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: \: 6pq - 2q}}}$

If it's telling to do this further, then group the common factor:

$\bf{3 \times 2pq - 2q}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: \: 2q(3p - 1)}}}$

c) For this, just factor out the terms, and obtain the final answer:

$\bf{\dfrac{x^2 + 5x + 6}{x + 2}}$

$\bf{\dfrac{(x^2 + 2x) + (3x + 6)}{x + 2}}$

$\bf{\dfrac{x(x + 2) + 3(x + 2)}{x + 2}}$

$\bf{\dfrac{(x + 2)(x + 3)}{x + 2}}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Answer: \: \: (x + 3)}}}$

Hope it helps and clears the doubts for simplifying the given terms!!!!!