(8m^7 - 10m^5) / 2m^3
Answer choices - 4m^7 - 5m^5
4m^4 - 10m^5
8m^7 - 10m^2
4m^4 - 5m^2,
please show me your work
Simplify into one fraction
-2/x+3 - 4/x-5
answer choices - -6x - 2/ (x+3)(x-5)
6(x-1)/(x+3)(x-5)
-6/(x+3)(x-5)
Simplify into on fraction
7/x-3 + 3/x-5
answer choices : -10x - 44/ (x-3)(x-5)
10x - 44/ (x-3)(x-5)
10x/(x-3)(x-5)
Simplify into one fraction
-1/x-9 - -2/x+7
Answer choices - 1/(x-9)(x+7)
-3/(x-9)(x+7)
x - 25/(x-9)(x+7)
To simplify the expression (8m^7 - 10m^5) / 2m^3, we can divide each term by 2m^3.
Step 1: Divide 8m^7 by 2m^3:
8m^7 / 2m^3 = 4m^(7-3) = 4m^4
Step 2: Divide -10m^5 by 2m^3:
-10m^5 / 2m^3 = -5m^(5-3) = -5m^2
Therefore, the simplified expression is 4m^4 - 5m^2.
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To simplify the expression -2/(x+3) - 4/(x-5), we need to find a common denominator for the fractions.
Step 1: Find the least common multiple (LCM) of (x+3) and (x-5):
The LCM of (x+3) and (x-5) is (x+3)(x-5).
Step 2: Rewrite each fraction with the common denominator:
-2/(x+3) can be rewritten as -2(x-5)/[(x+3)(x-5)]
-4/(x-5) can be rewritten as -4(x+3)/[(x+3)(x-5)]
Step 3: Combine the fractions:
-2(x-5)/[(x+3)(x-5)] - 4(x+3)/[(x+3)(x-5)] = (-2x + 10 - 4x - 12)/[(x+3)(x-5)]
= (-6x - 2)/[(x+3)(x-5)]
Therefore, the simplified expression is -6x - 2/[(x+3)(x-5)].
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To simplify the expression 7/(x-3) + 3/(x-5), we also need to find a common denominator.
Step 1: Find the least common multiple (LCM) of (x-3) and (x-5):
The LCM of (x-3) and (x-5) is (x-3)(x-5).
Step 2: Rewrite each fraction with the common denominator:
7/(x-3) can be rewritten as 7(x-5)/[(x-3)(x-5)]
3/(x-5) can be rewritten as 3(x-3)/[(x-3)(x-5)]
Step 3: Combine the fractions:
7(x-5)/[(x-3)(x-5)] + 3(x-3)/[(x-3)(x-5)] = (7x - 35 + 3x - 9)/[(x-3)(x-5)]
= (10x - 44)/[(x-3)(x-5)]
Therefore, the simplified expression is (10x - 44)/[(x-3)(x-5)].
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To simplify the expression -1/(x-9) - (-2)/(x+7), we can simplify the subtraction.
Step 1: Remove the parentheses around -2/(x+7) and change the sign:
-1/(x-9) + 2/(x+7)
Step 2: Find a common denominator for the fractions.
Step 3: Find the least common multiple (LCM) of (x-9) and (x+7):
The LCM of (x-9) and (x+7) is (x-9)(x+7).
Step 4: Rewrite each fraction with the common denominator:
-1/(x-9) can be rewritten as -1(x+7)/[(x-9)(x+7)]
2/(x+7) can be rewritten as 2(x-9)/[(x-9)(x+7)]
Step 5: Combine the fractions:
-1(x+7)/[(x-9)(x+7)] + 2(x-9)/[(x-9)(x+7)] = (-x - 7 + 2x - 18)/[(x-9)(x+7)]
= (x - 25)/[(x-9)(x+7)]
Therefore, the simplified expression is (x - 25)/[(x-9)(x+7)].
Let's solve each problem step by step:
1) (8m^7 - 10m^5) / 2m^3
To simplify this expression, we can distribute the division operator to each term in the numerator:
8m^7 / 2m^3 - 10m^5 / 2m^3
Next, we can simplify each term separately:
8 / 2 * m^7 / m^3 - 10 / 2 * m^5 / m^3
This simplifies to:
4 * m^(7-3) - 5 * m^(5-3)
4 * m^4 - 5 * m^2
Therefore, the answer is: 4m^4 - 5m^2.
2) -2/(x+3) - 4/(x-5)
To simplify this expression, we need to find a common denominator:
The common denominator is (x+3)(x-5).
Now we can rewrite each fraction with the common denominator:
-2(x-5)/[(x+3)(x-5)] - 4(x+3)/[(x+3)(x-5)]
Next, we can expand and combine the numerators:
[-2x + 10 - 4x - 12]/[(x+3)(x-5)]
Simplifying the numerator gives:
(-6x - 2)/[(x+3)(x-5)]
Therefore, the answer is: -6x - 2/[(x+3)(x-5)].
3) 7/(x-3) + 3/(x-5)
To simplify this expression, we need to find a common denominator:
The common denominator is (x-3)(x-5).
Now we can rewrite each fraction with the common denominator:
7(x-5)/[(x-3)(x-5)] + 3(x-3)/[(x-3)(x-5)]
Next, we can expand and combine the numerators:
[7x - 35 + 3x - 9]/[(x-3)(x-5)]
Simplifying the numerator gives:
(10x - 44)/[(x-3)(x-5)]
Therefore, the answer is: (10x - 44)/[(x-3)(x-5)].
4) -1/(x-9) - (-2)/(x+7)
To simplify this expression, we need to work with the negative signs:
The expression becomes: -1/(x-9) + 2/(x+7)
To find a common denominator, we multiply the denominators together:
The common denominator is (x-9)(x+7).
Now we can rewrite each fraction with the common denominator:
-1(x+7)/[(x-9)(x+7)] + 2(x-9)/[(x-9)(x+7)]
Next, we can combine the numerators:
[-x - 7 + 2x - 18]/[(x-9)(x+7)]
Simplifying the numerator gives:
(x - 25)/[(x-9)(x+7)]
Therefore, the answer is: (x - 25)/[(x-9)(x+7)].
(8m^7 - 10m^5) / 2m^3
= 8m^7/2m^3 - 10m^5/2m^3
= 4m^4 - 5m^2
-2/(x+3) - 4/(x-5)
= [-2(x-5) - 4(x+3)] / (x+3)(x-5)
. . .
7/(x-3) + 3/(x-5)
= [7(x-5) + 3(x-3)] / (x+5)(x-3)
. . .
-1/(x-9) - -2/(x+7)
= [-(x+7) + 2(x-9)] / (x-9)(x+7)
. . .