Question

Help me with 16,17,18,and 19 please simpl

Answer 1

Ques 16)

We have to simplify the expression:

`(t^2)/(t^2+3t-18)-((5t)/(t^2+3t-18)-(t-3)/(t^2+3t-18))\\   \\=(t^2)/(t^2+3t-18)-((4t+3)/(t^2+3t-18))\\  \\=(t^2-4t-3)/(t^2+3t+18)`

Ques 17)

`(3w^2+7w-7)/(w^2+8w+15)+(2w^2-9w+4)/((2w^2+9w-5)(w^2-w-12))\\  \\=(3w^2+7w-7)/(w^2+8w+15)+((2w-1)(w-4))/((2w-1)(w+5)(w+3)(w-4))\\\\=(3w^2+7w-7)/((w+3)(w+5))+(1)/((w+3)(w+5))\\\\=(3w^2+7w-7+1)/((w+3)(w+5))\\\\=((3w-2)(w+3))/((w+5)(w+3))\\\\=(3w-2)/(w+5)`

Ques 18)

Let the blank space be denoted by the quantity 'x'.

`(x)/(12a^2+8a)+(15a^2)/(12a^2+8a)=(7a)/(3a+2)\\ \\(x+15a^2)/(12a^2+8a)=(7a)/(3a+2)\\\\=(x+15a^2)/(4a(3a+2))=(7a)/(3a+2)\\\\=(x+15a^2)/(4a)=7a\\\\x+15a^2=28a^2\\\\x=28a^2-15a^2\\\\x=13a^2`

Ques 19)

Let the missing quantity be denoted by 'x'.

`(p^2+7p+2)/(p^2+5p-14)-(x)/(p^2+5p-14)=(p-1)/(p-2)\\ \\(p^2+7p+2-x)/(p^2+5p-14)=(p-1)/(p-2)\\\\(p^2+7p+2-x)/((p-2)(p+7))=(p-1)/(p-2)\\\\p^2+7p+2-x=(p-1)(p+7)\\\\p^2+7p+2-x=p^2+6p-7\\\\x=p+9`