Simplify into one fraction.
start fraction 7 over x minus 3 end fraction plus start fraction 3 over x plus 5 end fraction
A. start fraction 10 over left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis end fraction
B. start fraction 10 x plus 26 over left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis end fraction
C. start fraction 10 over 2 x plus 2 end fraction
D. start fraction 10 x plus 44 over left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis end fraction
The answer is A. To combine the two fractions, we need a common denominator of (x - 3)(x + 5). Thus, we have:
start fraction 7(x + 5) over (x - 3)(x + 5) end fraction + start fraction 3(x - 3) over (x - 3)(x + 5) end fraction
Combining the numerators, we have:
start fraction 7x + 35 + 3x - 9 over (x - 3)(x + 5) end fraction
Simplifying the numerator, we have:
start fraction 10x + 26 over (x - 3)(x + 5) end fraction
Now, we have a single fraction, which can be simplified no further.
Solve.
The quotient 4 over x plus the quotient 5 over x equals negative 3
A. x equals 27
B. x equals 3
C. x equals negative 3
D. x equals negative 27
To solve, we need to combine the two quotients into a single fraction. We have:
start fraction 4 over x end fraction + start fraction 5 over x end fraction = start fraction 4 + 5 over x end fraction = start fraction 9 over x end fraction
Now, we can set up the equation:
start fraction 9 over x end fraction = -3
Multiplying both sides by x, we have:
9 = -3x
Dividing both sides by -3, we have:
x = -3
Therefore, the answer is C.
To simplify the expression, we need to find the common denominator for the two fractions. In this case, the common denominator is (x - 3)(x + 5).
Next, we can rewrite the fractions with the common denominator:
7/(x - 3) + 3/(x + 5) = (7(x + 5))/((x - 3)(x + 5)) + (3(x - 3))/((x - 3)(x + 5))
Combining the fractions:
= (7x + 35 + 3x - 9)/((x - 3)(x + 5))
Simplifying the numerator:
= (10x + 26)/((x - 3)(x + 5))
Therefore, the answer is (B) start fraction 10 x plus 26 over left parenthesis x minus 3 right parenthesis left parenthesis x plus 5 right parenthesis end fraction.