factorisation - help!

a. pq + h = ph-q / p-2 ==> express q in terms of p and h.

(answer is q= 2h/(p-1)^2)

b. 4s^2 + 4s - r^2 +1

(answer is 25-x/(x-3)(x+2))

thanks!

b. 4s^2 + 4s - r^2 +1

(answer is 25-x/(x-3)(x+2))

what is this. s/x?

pq + h = ph-q / p-2

what is the fraction here? ph-q / p-2 or ph= (q/(p-2))

a. pq + h = ph-q / p-2 ==> express q in terms of p and h.

(answer is q= 2h/(p-1)^2)

(p-2)(pq + h) = ph - q

p^2q + hp - 2pq - 2h = ph - q

p^2q - 2pq + q = ph + 2h - hp

q (p^2 - 2p + 1) = 2h

q = 2h / (p-1)^2

b. 4s^2 + 4s - r^2 +1

(answer is 25-x/(x-3)(x+2))

how come there's s, r and x? i think you type wrongly

thanks!

pq + h = ph-q / p-2

(pq + h)( p-2) = ph-q

p^2q - 2pq +ph-2h = ph -q

p^2q - 2pq + q = 2h

q(p^2 - 2p + 1) = 2h

q(p-1)^2 = 2h

q= 2h/(p-1)^2

4s^2 + 4s - r^2 +1

4s(s+1) + (1^2 - r^2)

4s(s +1) + (1+r)(1-r)