16 (a) Simplify - OCR - GCSE Maths - Question 16 - 2017 - Paper 1
Question 16
16 (a) Simplify.
$$\frac{3y^3}{y^{-4}}$$
(b) Write as a single fraction in its simplest form.
$$\frac{3}{x-1} + \frac{4}{x+2}$$
Worked Solution & Example Answer:16 (a) Simplify - OCR - GCSE Maths - Question 16 - 2017 - Paper 1
Simplify.
$$\frac{3y^3}{y^{-4}}$$
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To simplify the expression, we apply the laws of exponents. Recall that (a^{-n} = \frac{1}{a^n}) which will allow us to rewrite the denominator:
y−43y3=3y3−(−4)=3y3+4=3y7.
Thus, the simplified answer is (3y^{7}).
Write as a single fraction in its simplest form.
$$\frac{3}{x-1} + \frac{4}{x+2}$$
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To combine the fractions, we first identify the common denominator, which will be ((x-1)(x+2)):
x−13+x+24=(x−1)(x+2)3(x+2)+(x−1)(x+2)4(x−1).
Next, we expand the numerators:
dollars
\frac{3(x+2) + 4(x-1)}{(x-1)(x+2)} = \frac{3x + 6 + 4x - 4}{(x-1)(x+2)} = \frac{7x + 2}{(x-1)(x+2)}.
Therefore, the single fraction in its simplest form is \(\frac{7x + 2}{(x-1)(x+2)}\).Join the GCSE students using SimpleStudy...
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