Simplify: (3x + 15) / (5x + 25)
Answers
Answer:
The required answer is 3/5.
Step-by-step explanation:
Given : (3x + 15) / (5x + 25)
To find : we need to find the simplest value.
Solution :
For simplifying this, we need to take the conjugate of the denominator.
That is , the sign in the denominator term is changed and that term is multiplied both in the numerator and the denominator.
Now taking conjugate, 3x + 15 = 3x + 15 × 5x - 25
5x + 25 5x +25 5x -25
=(3x + 15)×(5x - 25)
(5x +25)×(5x - 25)
=3x ×5x +3x × (-25) +15 × 5x + 15 ×(-25)
(5x)² - (25)²
=15x²-75x + 75x - 375
25x²- 625
=15x²-375 = 15(x² - 25)
25x²-625 25(x²-25)
= 15/25 = 3/5.
∴ The required answer is 3/5.
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Answer:
The simplified value of (3x + 15)/(5x + 25) is 3/5.
Step-by-step explanation:
Step 1 of 4
Consider the given expression as follows:
(3x + 15)/(5x + 25)
Notice that the given expression is in the fraction form.
Here, numerator = 3x + 15 and denominator = 5x + 25
Step 2 of 4
Consider the numerator as follows:
3x + 15
Rewrite as follows:
3(x + 5) . . . . . (i)
Step 3 of 4
Now, consider the denominator as follows:
5x + 25
Rewrite as follows:
5(x + 5) . . . . . (ii)
Step 4 of 4
The simplified value of the expression (3x + 15)/(5x + 25).
From (i) and (ii), the given expression becomes,
3(x + 5)/5(x + 5)
3/5
Therefore, the required answer is 3/5.
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