19. The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2,
the fraction is increased by 1/12Find the original fraction.

Let the original fraction be

Now let's increase both numerator and denominator by 2:

This produces a 1/12 increase:

The left hand side can be rearranged as

Invert both sides:

Solve the quadratic equation:

So, in the first case, the original fraction is

In the second case, we have

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

explanation:

step-by-step explanation: