Answer:
Step-by-step explanation:
7) 2ab + 4ac = 2*a*b + 2 *2 *a*c
= 2a(b + 2c)
[tex]\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}[/tex]
8) ac - a²c² = c( a - a²c)
bc - abc = c(b - ab)
[tex]\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\[/tex]
[tex]=\dfrac{a-a^{2}c}{b-abc}[/tex]
9) b²+ 4b - 5 = b² + 5b - 1b - 5
= b(b + 5) - 1(b + 5)
= (b +5)(b - 1)
b² + 8b + 15 = b² + 5b + 3b + 15
= b(b + 5) + 3(b + 5)
= (b + 5 )(b + 3)
[tex]\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\[/tex]
[tex]=\dfrac{b-1}{b+3}[/tex]
