Which term can be cancelled out of the expression

Mathematics

1 answer:

Lubov Fominskaja [6]4 years ago

5 0

Answer:

x+3

Step-by-step explanation:

If you factor 5 out of the denominator of the first expression, 5x+15 turns into 5(x+3).

Then, since you have x+3 in the numerator and denominator, it will cancel out.

The steps are shown below:

$\frac{7x}{5x+15} *\frac{x+3}{8} \\\\=\frac{7x}{5(x+3)} *\frac{x+3}{8} \\\\=\frac{7x}{5} *\frac{1}{8} \\\\=\frac{7x}{40}\\$

Ive attached an image that shows an example of simplifying an expression using a the same technique.

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Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 m

weqwewe [10]

Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Answer:

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

$r = \frac{d}{t} \\\\t = \frac{d}{r} \\\\t = \frac{160}{r} \\\\$

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

$\frac{160}{(r-4)} = \frac{160}{r} + 2 \\\\$

Simplify the equation

$\frac{160}{(r-4)} - \frac{160}{r} = 2 \\\\\frac{160r - 160(r-4)}{r(r-4)} = 2 \\\\\frac{160r - 160r+640)}{r(r-4)} = 2 \\\\160r - 160r+640 = r(r-4) (2) \\\\640 = r(r-4) (2) \\\\640 = (r^2 - 4r) (2) \\\\640 = 2r^2 - 8r \\\\2r^2 - 8r-640 =0 \\\\2(r^2 - 4r-320) =0 \\\\r^2 - 4r-320 =0 \\\\$