What is the difference start fraction 5x minus 2 over 4x end fraction minus start fraction x minus 2 over 4x end fraction ?
The difference between start fraction 5x minus 2 over 4x end fraction and start fraction x minus 2 over 4x end fraction is:
start fraction 5x minus 2 over 4x end fraction minus start fraction x minus 2 over 4x end fraction
= start fraction 5x over 4x end fraction - start fraction 2 over 4x end fraction - start fraction x over 4x end fraction + start fraction 2 over 4x end fraction
= start fraction 4x over 4x end fraction + start fraction 3x over 4x end fraction - start fraction 2 over 4x end fraction
= start fraction 7x over 4x end fraction - start fraction 2 over 4x end fraction
= start fraction 7x - 2 over 4x end fraction
Therefore, the difference between start fraction 5x minus 2 over 4x end fraction and start fraction x minus 2 over 4x end fraction is start fraction 7x - 2 over 4x end fraction.
start fraction 7x - 2 over 4x end fraction simplified
start fraction 7x - 2 over 4x end fraction can be simplified by dividing the numerator and denominator by the greatest common factor, which in this case is 1:
start fraction 7x - 2 over 4x end fraction = (7x - 2)/(4x)
What is the sum start fraction 1 over 2b end fraction plus start fraction b over 2 end fraction ?
The sum of start fraction 1 over 2b end fraction and start fraction b over 2 end fraction is:
start fraction 1 over 2b end fraction + start fraction b over 2 end fraction
To add these fractions, we need a common denominator. The least common multiple of 2b and 2 is 2b, so we can rewrite the fractions with the common denominator of 2b:
start fraction 1 over 2b end fraction + start fraction b over 2 end fraction = start fraction 1 times b over 2b times b end fraction + start fraction b times 2b over 2 times b times 2 end fraction
= start fraction b over 2b² end fraction + start fraction 2b over 4b² end fraction
Then, we can add the two fractions by getting a common denominator:
start fraction b over 2b² end fraction + start fraction 2b over 4b² end fraction = start fraction 2b + b times 2 end fraction over 4b²
= start fraction 4b end fraction over 4b²
= start fraction 1 end fraction over b
Therefore, the sum of start fraction 1 over 2b end fraction and start fraction b over 2 end fraction is equal to start fraction 1 end fraction over b.
What is the sum start fraction 1 over g plus 2 end fraction plus start fraction 3 over g plus 1 end fraction ?
To find the sum of start fraction 1 over g plus 2 end fraction and start fraction 3 over g plus 1 end fraction, we need to get a common denominator:
start fraction 1 over g plus 2 end fraction + start fraction 3 over g plus 1 end fraction = start fraction 1 times (g + 1) over (g + 2) times (g + 1) end fraction + start fraction 3 times (g + 2) over (g + 1) times (g + 2) end fraction
= start fraction g + 1 over (g + 2)(g + 1) end fraction + start fraction 3g + 6 over (g + 1)(g + 2) end fraction
Now, we can combine the two fractions:
start fraction g + 1 over (g + 2)(g + 1) end fraction + start fraction 3g + 6 over (g + 1)(g + 2) end fraction = start fraction (g + 1) + (3g + 6) over (g + 2)(g + 1) end fraction
= start fraction 4g + 7 over (g + 2)(g + 1) end fraction
Therefore, the sum of start fraction 1 over g plus 2 end fraction and start fraction 3 over g plus 1 end fraction is equal to start fraction 4g + 7 over (g + 2)(g + 1) end fraction.
What is the difference start fraction r plus 2 over r plus 4 end fraction minus start fraction 3 over r plus 1 end fraction ?
The difference between start fraction r plus 2 over r plus 4 end fraction and start fraction 3 over r plus 1 end fraction is:
start fraction r plus 2 over r plus 4 end fraction - start fraction 3 over r plus 1 end fraction
To subtract these fractions, we need to get a common denominator, which is (r + 4)(r + 1):
start fraction r + 2 over r + 4 end fraction - start fraction 3 over r + 1 end fraction = start fraction (r + 2)(r + 1) over (r + 4)(r + 1) end fraction - start fraction 3(r + 4) over (r + 4)(r + 1) end fraction
= start fraction (r² + 3r + 2) over (r + 4)(r + 1) end fraction - start fraction (3r + 12) over (r + 4)(r + 1) end fraction
Now, we can combine the two fractions by subtracting them:
start fraction (r² + 3r + 2) over (r + 4)(r + 1) end fraction - start fraction (3r + 12) over (r + 4)(r + 1) end fraction = start fraction (r² + 3r + 2 - 3r - 12) over (r + 4)(r + 1) end fraction
= start fraction (r² - 10) over (r + 4)(r + 1) end fraction
Therefore, the difference between start fraction r plus 2 over r plus 4 end fraction and start fraction 3 over r plus 1 end fraction is equal to start fraction (r² - 10) over (r + 4)(r + 1) end fraction.