Question 30 of 43advanced🔧 ApplyShort Answer5 marks

Simplify the following rational expressions assuming that the expressions in the denominators are not equal to zero:

(i)

(3p23p^{2} - 3pq - 18q218q^{2}) / (p2p^{2} + 3pq - 10q210q^{2})

Answer

3(p - 3q)(p + 2q) / ((p + 5q)(p - 2q))

(ii)

(n3n^{3} - 3n2m3n^{2m} + 3nm23nm^{2} - m3m^{3}) / (5m25m^{2} - 10mn + 5n25n^{2})

Answer

(n - m) / 5

(iii)

(w3w^{3} - v3v^{3} + x3x^{3} + 3wvx) / (w2w^{2} + v2v^{2} + x2x^{2} - 2wv - 2vx + 2wx)

Answer

(w² + v² + x² + wv + vx - wx) / (w - v + x)

(iv)

(4y24y^{2} - 20yz + 25z225z^{2}) / (25z225z^{2} - 4y24y^{2})

Answer

(5z - 2y) / (5z + 2y)

(v)

((x2x^{2} + x - 6)(x2x^{2} - 7x + 12)) / ((x2x^{2} - 6x + 8)(x2x^{2} - 9))

Answer

1

Explanation

To simplify rational expressions, we factorize the numerators and denominators using algebraic identities and the middle term splitting method, then cancel the common factors. For (i), we split the middle term. For (ii), we use the (a-b)³ identity. For (iii), we apply the a³+b³+c³-3abc identity and recognize the denominator as a perfect square. For (iv), we use the perfect square and difference of squares identities. For (v), we factorize all four quadratic expressions to find that all terms cancel out.

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